Archive for rational mechanics and analysis, ISSN 1432-0673, 2019, Volume 234, Issue 2, pp. 727 - 775

We establish the vanishing viscosity limit of the Navier–Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DERIVATION | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | MODELS | CLASSICAL-SOLUTIONS | KORTEWEG | SHALLOW-WATER EQUATIONS | Viscosity | Three dimensional flow | Fluid dynamics | Mathematical analysis | Fluid flow | Inviscid flow | Euler-Lagrange equation | Navier-Stokes equations | Compressible fluids | Viscous flow

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | DERIVATION | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | MODELS | CLASSICAL-SOLUTIONS | KORTEWEG | SHALLOW-WATER EQUATIONS | Viscosity | Three dimensional flow | Fluid dynamics | Mathematical analysis | Fluid flow | Inviscid flow | Euler-Lagrange equation | Navier-Stokes equations | Compressible fluids | Viscous flow

Journal Article

Multibody system dynamics, ISSN 1573-272X, 2018, Volume 45, Issue 1, pp. 87 - 103

It is well known that the projective Newton–Euler equation and the Lagrange equation of second kind lead to the same result when deriving the dynamical equations of motion for holonomic rigid multibody systems...

Lagrangian dynamics | Engineering | Vibration, Dynamical Systems, Control | Spatial rigid multibody systems | Constrained motion | Automotive Engineering | Mechanical Engineering | Optimization | Electrical Engineering | Newton–Euler equations | Newton-Euler equations | MECHANICS

Lagrangian dynamics | Engineering | Vibration, Dynamical Systems, Control | Spatial rigid multibody systems | Constrained motion | Automotive Engineering | Mechanical Engineering | Optimization | Electrical Engineering | Newton–Euler equations | Newton-Euler equations | MECHANICS

Journal Article

Nonlinear differential equations and applications, ISSN 1420-9004, 2018, Volume 25, Issue 5, pp. 1 - 15

...:475–485, 1985) developed for the Euler equations, we extend the formation of singularities of classical solution to the 3D Euler equations established in Makino et al. (Jpn J Appl Math 3:249–257, 1986) and Sideris (1985...

Fast decay weight | 35L40 | Spherically symmetric solutions | Analysis | Averaged quantity | Mathematics | 35L45 | 58J45 | 58J47 | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs

Fast decay weight | 35L40 | Spherically symmetric solutions | Analysis | Averaged quantity | Mathematics | 35L45 | 58J45 | 58J47 | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs

Journal Article

International Journal of Modern Physics D, ISSN 0218-2718, 05/2017, Volume 26, Issue 6, p. 1750047

Mathisson–Papapetrou–Tulczyjew–Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity...

Spinning particle | ultra-relativistic motion | gravimagnetic moment | FIELDS | GENERAL-RELATIVITY | SPIN | PARTICLES | FRENKEL ELECTRON | RADIATION | MOTION | ASTRONOMY & ASTROPHYSICS | BODIES | COMPACT BINARY-SYSTEMS

Spinning particle | ultra-relativistic motion | gravimagnetic moment | FIELDS | GENERAL-RELATIVITY | SPIN | PARTICLES | FRENKEL ELECTRON | RADIATION | MOTION | ASTRONOMY & ASTROPHYSICS | BODIES | COMPACT BINARY-SYSTEMS

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2015, Volume 80, Issue 1-2, pp. 791 - 802

A new technique for constructing conservation laws for fractional differential equations not having a Lagrangian is proposed...

Conservation law | Nonlinear self-adjointness | Time-fractional diffusion equation | Symmetry | MECHANICS | CALCULUS | NOETHERS THEOREM | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | EULER-LAGRANGE | Environmental law | Analysis | Conservation laws | Operators (mathematics) | Mathematical analysis | Differential equations | Wave equations | Lie groups | Derivatives | Diffusion | Operators | Construction | Nonlinearity | Evolution

Conservation law | Nonlinear self-adjointness | Time-fractional diffusion equation | Symmetry | MECHANICS | CALCULUS | NOETHERS THEOREM | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | EULER-LAGRANGE | Environmental law | Analysis | Conservation laws | Operators (mathematics) | Mathematical analysis | Differential equations | Wave equations | Lie groups | Derivatives | Diffusion | Operators | Construction | Nonlinearity | Evolution

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2017, Volume 223, Issue 1, pp. 301 - 417

We study the inviscid limit of the free boundary Navier–Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | WATER-WAVES | MATHEMATICS, APPLIED | MECHANICS | MOTION | INCOMPRESSIBLE FLUID | WELL-POSEDNESS | EULER-EQUATIONS | TENSION LIMIT | FREE-BOUNDARY PROBLEM | LAYERS | Asymptotic series | Fluid dynamics | Mathematical analysis | Fluid flow | Euler-Lagrange equation | Free boundaries | Free surfaces | Navier-Stokes equations | Viscosity | Intervals | Asymptotic expansions | Euler equations | Regularity | Analysis of PDEs | Mathematics

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | WATER-WAVES | MATHEMATICS, APPLIED | MECHANICS | MOTION | INCOMPRESSIBLE FLUID | WELL-POSEDNESS | EULER-EQUATIONS | TENSION LIMIT | FREE-BOUNDARY PROBLEM | LAYERS | Asymptotic series | Fluid dynamics | Mathematical analysis | Fluid flow | Euler-Lagrange equation | Free boundaries | Free surfaces | Navier-Stokes equations | Viscosity | Intervals | Asymptotic expansions | Euler equations | Regularity | Analysis of PDEs | Mathematics

Journal Article

7.
Full Text
Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives

Journal of optimization theory and applications, ISSN 1573-2878, 2016, Volume 174, Issue 1, pp. 256 - 275

Two variational problems of finding the Euler–Lagrange equations corresponding to Lagrangians containing fractional derivatives of real- and complex-order are considered...

Mathematics | Theory of Computation | Complex-order fractional variational problems | Optimization | 70H03 | Weak convergence | 70G75 | Calculus of Variations and Optimal Control; Optimization | Euler–Lagrange equations | Expansion formula | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49K05 | 49K15 | SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Euler-Lagrange equations | NOETHERS THEOREM | FORMULATION | Lagrange multiplier | Approximation | Mathematical analysis | Integrals | Optimal control | Kinetics | Derivatives

Mathematics | Theory of Computation | Complex-order fractional variational problems | Optimization | 70H03 | Weak convergence | 70G75 | Calculus of Variations and Optimal Control; Optimization | Euler–Lagrange equations | Expansion formula | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49K05 | 49K15 | SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Euler-Lagrange equations | NOETHERS THEOREM | FORMULATION | Lagrange multiplier | Approximation | Mathematical analysis | Integrals | Optimal control | Kinetics | Derivatives

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2013, Volume 399, Issue 1, pp. 239 - 251

...–Lagrange equations of the type: (ELα)∂L∂x(u,D−αu,t)+D+α(∂L∂y(u,D−αu,t))=0, on a real interval [a,b] and where D−α and D+α...

Fractional Euler–Lagrange equations | Fractional variational calculus | Existence | Fractional Euler-Lagrange equations | MATHEMATICS | MATHEMATICS, APPLIED | MECHANICS | CALCULUS | DIFFERENTIAL-EQUATIONS | FORMULATION | DERIVATIVES

Fractional Euler–Lagrange equations | Fractional variational calculus | Existence | Fractional Euler-Lagrange equations | MATHEMATICS | MATHEMATICS, APPLIED | MECHANICS | CALCULUS | DIFFERENTIAL-EQUATIONS | FORMULATION | DERIVATIVES

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2017, Volume 473, Issue 2200, p. 20170063

Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water...

Spherical coordinates | Euler equations | Gyres | gyres | spherical coordinates | MULTIDISCIPLINARY SCIENCES | 1008 | 119 | 140

Spherical coordinates | Euler equations | Gyres | gyres | spherical coordinates | MULTIDISCIPLINARY SCIENCES | 1008 | 119 | 140

Journal Article

11.
Full Text
A new flux‐limiting approach–based kinetic scheme for the Euler equations of gas dynamics

International journal for numerical methods in fluids, ISSN 1097-0363, 2019, Volume 90, Issue 1, pp. 22 - 56

Summary This paper proposes a new kinetic‐theory‐based high‐resolution scheme for the Euler equations of gas dynamics...

Collisionless Boltzmann equation | flux‐limiting approach | Euler equations | compressible flow | flux-limiting approach | RIEMANN SOLVER | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SIMULATION | FLOW | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LIMITERS | Accuracy | Fluctuations | Methodology | Robustness (mathematics) | Dynamics | Gas dynamics | Boltzmann transport equation | Fluxes | Kinetic theory | Euler-Lagrange equation | Equations | Resolution

Collisionless Boltzmann equation | flux‐limiting approach | Euler equations | compressible flow | flux-limiting approach | RIEMANN SOLVER | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SIMULATION | FLOW | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LIMITERS | Accuracy | Fluctuations | Methodology | Robustness (mathematics) | Dynamics | Gas dynamics | Boltzmann transport equation | Fluxes | Kinetic theory | Euler-Lagrange equation | Equations | Resolution

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 6/2008, Volume 52, Issue 4, pp. 331 - 335

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles...

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | Mechanics | Fractional variational calculus | Mechanical Engineering | Differential equations of fractional order | Fractional calculus | fractional variational calculus | FIELDS | fractional calculus | MECHANICS | SEQUENTIAL MECHANICS | differential equations of fractional order | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | Euler-Lagrange equation | Variational principles | Mathematical analysis | Exact solutions | Differential equations

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | Mechanics | Fractional variational calculus | Mechanical Engineering | Differential equations of fractional order | Fractional calculus | fractional variational calculus | FIELDS | fractional calculus | MECHANICS | SEQUENTIAL MECHANICS | differential equations of fractional order | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | Euler-Lagrange equation | Variational principles | Mathematical analysis | Exact solutions | Differential equations

Journal Article

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 04/2018, Volume 376, Issue 2118, p. 20170222

This paper addresses the main issue of Hilbert's sixth problem, namely the rigorous passage of solutions to the mesoscopic Boltzmann equation to macroscopic solutions of the Euler equations of compressible gas dynamics...

Boltzmann equation | Kinetic equations | Capillarity | Korteweg equations | Navier-Stokes equations | MULTIDISCIPLINARY SCIENCES | HYDRODYNAMICS | RAREFIED-GAS | kinetic equations | NUMERICAL-ANALYSIS | capillarity | NONUNIFORM SYSTEM | THERMAL CREEP | FLOWS | FREE-ENERGY | EQUATION | VELOCITIES | Navier–Stokes equations | 1009

Boltzmann equation | Kinetic equations | Capillarity | Korteweg equations | Navier-Stokes equations | MULTIDISCIPLINARY SCIENCES | HYDRODYNAMICS | RAREFIED-GAS | kinetic equations | NUMERICAL-ANALYSIS | capillarity | NONUNIFORM SYSTEM | THERMAL CREEP | FLOWS | FREE-ENERGY | EQUATION | VELOCITIES | Navier–Stokes equations | 1009

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2019, Volume 77, Issue 4, pp. 1216 - 1231

.... By realizing that the excessive numerical dissipations corresponding to the velocity-difference terms of the momentum equations make these schemes incapable of obtaining physical solutions at low...

HLLEMS-AS | Shock anomaly | All speeds | Computational fluid dynamics | UPWIND SCHEMES | MATHEMATICS, APPLIED | ACCURATE | RIEMANN SOLVER | PRESSURE FLUX | BEHAVIOR | FORMULATION | GODUNOV-TYPE METHODS | IMPROVEMENT | FLOWS | EFFICIENT | Discontinuity | Sound waves | Turbulent flow | Robustness (mathematics) | Energy dissipation | Low speed | Inviscid flow | Aerodynamics | Euler-Lagrange equation | Cylinders

HLLEMS-AS | Shock anomaly | All speeds | Computational fluid dynamics | UPWIND SCHEMES | MATHEMATICS, APPLIED | ACCURATE | RIEMANN SOLVER | PRESSURE FLUX | BEHAVIOR | FORMULATION | GODUNOV-TYPE METHODS | IMPROVEMENT | FLOWS | EFFICIENT | Discontinuity | Sound waves | Turbulent flow | Robustness (mathematics) | Energy dissipation | Low speed | Inviscid flow | Aerodynamics | Euler-Lagrange equation | Cylinders

Journal Article

The Astrophysical journal, ISSN 1538-4357, 05/2019, Volume 877, Issue 2, p. 113

We investigate the vorticity-preserving properties of the compressible, second-order residual-based scheme, “RBV2.” The scheme has been extensively tested on...

Turbulence | Turbulent flow | Accretion | Compressibility | Computer simulation | Computational fluid dynamics | Shear flow | Fluid flow | Exact solutions | Protoplanetary disk | Aerodynamics | Euler-Lagrange equation | Accretion disks | Vortexes | Finite element method | Algorithms | Wavelengths | Mathematical analysis | Energy dissipation | Vortices | Vorticity | Acceleration

Turbulence | Turbulent flow | Accretion | Compressibility | Computer simulation | Computational fluid dynamics | Shear flow | Fluid flow | Exact solutions | Protoplanetary disk | Aerodynamics | Euler-Lagrange equation | Accretion disks | Vortexes | Finite element method | Algorithms | Wavelengths | Mathematical analysis | Energy dissipation | Vortices | Vorticity | Acceleration

Journal Article

1967, Schaum's outline series, 353

Book

AIAA Journal, ISSN 0001-1452, 11/2018, Volume 56, Issue 11, pp. 4437 - 4452

This study analyzes the behavior of solutions to the quasi-one-dimensional and two-dimensional adjoint Euler equations at singularities, including shocks, sonic points/lines, and sharp trailing edges...

SHAPE OPTIMIZATION | MESHES | APPROXIMATIONS | UNSTRUCTURED GRIDS | ADAPTATION | SENSITIVITIES | CONVERGENCE | AERODYNAMIC DESIGN OPTIMIZATION | FLOWS | ENGINEERING, AEROSPACE | FORMULATION | Economic models | Numerical analysis | Singularities | Euler-Lagrange equation | Dimensional analysis

SHAPE OPTIMIZATION | MESHES | APPROXIMATIONS | UNSTRUCTURED GRIDS | ADAPTATION | SENSITIVITIES | CONVERGENCE | AERODYNAMIC DESIGN OPTIMIZATION | FLOWS | ENGINEERING, AEROSPACE | FORMULATION | Economic models | Numerical analysis | Singularities | Euler-Lagrange equation | Dimensional analysis

Journal Article

Geoscientific Model Development, ISSN 1991-959X, 02/2017, Volume 10, Issue 2, pp. 791 - 810

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics...

GEOSCIENCES, MULTIDISCIPLINARY | GEOSTROPHIC ADJUSTMENT | COMPUTATIONAL MODES | FRAMEWORK | NUMERICAL-INTEGRATION | VORTICITY | GENERAL-METHOD | Hamiltonian systems | Research | Differential equations, Partial | Mathematical research | Shallow water equations | Compressibility | Fluid dynamics | Computer simulation | Methodology | Conservation | Water conservation | Rossby waves | Calculus | Euler-Lagrange equation | Properties | Shallow water | Equations | Polygons | Planetary waves | Conservation laws | Energy | Energy conservation | Enstrophy | Inertia | Mathematical models | Freshwater fish | Numerical models | Gravity | GEOSCIENCES

GEOSCIENCES, MULTIDISCIPLINARY | GEOSTROPHIC ADJUSTMENT | COMPUTATIONAL MODES | FRAMEWORK | NUMERICAL-INTEGRATION | VORTICITY | GENERAL-METHOD | Hamiltonian systems | Research | Differential equations, Partial | Mathematical research | Shallow water equations | Compressibility | Fluid dynamics | Computer simulation | Methodology | Conservation | Water conservation | Rossby waves | Calculus | Euler-Lagrange equation | Properties | Shallow water | Equations | Polygons | Planetary waves | Conservation laws | Energy | Energy conservation | Enstrophy | Inertia | Mathematical models | Freshwater fish | Numerical models | Gravity | GEOSCIENCES

Journal Article

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, ISSN 0218-2025, 03/2019, Volume 29, Issue 3, pp. 531 - 579

...) proposed by Chandrasekhar [S. Chandrasekhar, The post-Newtonian equations of hydrodynamics in general relativity, Astrophys. J. 142 (1965) 1488-1512...

SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | physical vacuum | Relativistic Euler equations | STABILITY | POST-NEWTONIAN EQUATIONS | HYDRODYNAMICS | WELL-POSEDNESS | CONSERVATION-LAWS | non-relativistic limits | local smooth solution | GLOBAL ENTROPY SOLUTIONS

SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | physical vacuum | Relativistic Euler equations | STABILITY | POST-NEWTONIAN EQUATIONS | HYDRODYNAMICS | WELL-POSEDNESS | CONSERVATION-LAWS | non-relativistic limits | local smooth solution | GLOBAL ENTROPY SOLUTIONS

Journal Article