2016, Mathematical surveys and monographs, ISBN 1470428571, Volume 214, xxiii, 515 pages

Book

2012, Graduate studies in mathematics, ISBN 0821872915, Volume 133, xix, 363

Book

2018, First edition., ISBN 0198794924, 162 pages

Book

2017, First edition., ISBN 9780465093779, viii, 221 pages

"Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1...

Mathematics | Euler's numbers | Euler, Leonhard, 1707-1783 | History | Numbers, Complex

Mathematics | Euler's numbers | Euler, Leonhard, 1707-1783 | History | Numbers, Complex

Book

Communications in mathematical physics, ISSN 1432-0916, 2014, Volume 330, Issue 3, pp. 1179 - 1225

In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | NONUNIQUENESS | INCOMPRESSIBLE EULER | NAVIER-STOKES EQUATIONS | CONSERVATION | DIMENSION | IDEAL HYDRODYNAMICS | ENERGY-DISSIPATION | PHYSICS, MATHEMATICAL | EULER EQUATIONS | CONJECTURE | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | NONUNIQUENESS | INCOMPRESSIBLE EULER | NAVIER-STOKES EQUATIONS | CONSERVATION | DIMENSION | IDEAL HYDRODYNAMICS | ENERGY-DISSIPATION | PHYSICS, MATHEMATICAL | EULER EQUATIONS | CONJECTURE | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

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

Journal of computational and applied mathematics, ISSN 0377-0427, 2015, Volume 290, pp. 370 - 384

Influenced by Higham et al. (2003), several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs...

Local Lipschitz condition | Strong convergence | Khasminskii-type condition | Truncated Euler–Maruyama method | Stochastic differential equation | Truncated Euler-Maruyama method | MATHEMATICS, APPLIED | NUMERICAL-INTEGRATION | SDES | STRONG-CONVERGENCE | Analysis | Methods | Differential equations | Lipschitz condition | Numerical analysis | Computation | Nonlinearity | Mathematical models | Stochasticity | Convergence

Local Lipschitz condition | Strong convergence | Khasminskii-type condition | Truncated Euler–Maruyama method | Stochastic differential equation | Truncated Euler-Maruyama method | MATHEMATICS, APPLIED | NUMERICAL-INTEGRATION | SDES | STRONG-CONVERGENCE | Analysis | Methods | Differential equations | Lipschitz condition | Numerical analysis | Computation | Nonlinearity | Mathematical models | Stochasticity | Convergence

Journal Article

Computers & fluids, ISSN 0045-7930, 10/2018, Volume 175, pp. 91 - 110

We present a numerical scheme for the solution of Euler equations based on staggered discretizations and working either on structured meshes or on general simplicial or tetrahedral/hexahedral meshes...

Finite elements | Finite volumes | Staggered discretizations | Euler equations | Compressible flows | Analysis | DISCONTINUOUS GALERKIN METHOD | VISCOSITY | 2-DIMENSIONAL RIEMANN PROBLEMS | FLOW | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FLUID | CELL | Algorithms | Numerical Analysis | Mathematics

Finite elements | Finite volumes | Staggered discretizations | Euler equations | Compressible flows | Analysis | DISCONTINUOUS GALERKIN METHOD | VISCOSITY | 2-DIMENSIONAL RIEMANN PROBLEMS | FLOW | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FLUID | CELL | Algorithms | Numerical Analysis | Mathematics

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2014, Volume 39, Issue 1, pp. 75 - 83

Painlevé equations are studied on the basis of linear equations, which are generic...

Heun deformed equation | 33E99 | Mathematics | Heun equation | 2×2 Fuchsian linear system | 33E17 | Euler integral transform | Antiquantization | 32S99 | Apparent singularity | Numerical Analysis | Analysis | 81R12 | Painlevé equation | 34B30

Heun deformed equation | 33E99 | Mathematics | Heun equation | 2×2 Fuchsian linear system | 33E17 | Euler integral transform | Antiquantization | 32S99 | Apparent singularity | Numerical Analysis | Analysis | 81R12 | Painlevé equation | 34B30

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2011, Volume 269, Issue 3, pp. 1137 - 1153

In this paper we present a geometric interpretation of the Degasperis–Procesi (DP) equation as the geodesic flow of a right-invariant symmetric linear connection on the diffeomorphism group of the circle...

Euler equation | 58D05 | Mathematics, general | Diffeomorphisms group of the circle | Mathematics | Degasperis–Procesi equation | 35Q53 | Degasperis-Procesi equation | MATHEMATICS | WATER-WAVES | CAMASSA-HOLM | MOTION | GEODESIC-FLOW | BLOW-UP PHENOMENA | WELL-POSEDNESS | WAVE BREAKING | SHOCK-WAVES | Mathematical Physics | Physics

Euler equation | 58D05 | Mathematics, general | Diffeomorphisms group of the circle | Mathematics | Degasperis–Procesi equation | 35Q53 | Degasperis-Procesi equation | MATHEMATICS | WATER-WAVES | CAMASSA-HOLM | MOTION | GEODESIC-FLOW | BLOW-UP PHENOMENA | WELL-POSEDNESS | WAVE BREAKING | SHOCK-WAVES | Mathematical Physics | Physics

Journal Article

Physica. D, ISSN 0167-2789, 2009, Volume 238, Issue 19, pp. 1975 - 1991

We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method...

Blow–up time | Separation | Complex singularities | Prandtl’s equations | Spectral methods | Regularizing viscosity | Blow-up time | Prandtl's equations | EXISTENCE | MATHEMATICS, APPLIED | INCOMPRESSIBLE EULER EQUATIONS | PHYSICS, MULTIDISCIPLINARY | ZERO VISCOSITY LIMIT | PHYSICS, MATHEMATICAL | FLOW | BOUNDARY-LAYER EQUATIONS | ANALYTIC SOLUTIONS | UNSTEADY SEPARATION | HALF-SPACE | NAVIER-STOKES SOLUTIONS

Blow–up time | Separation | Complex singularities | Prandtl’s equations | Spectral methods | Regularizing viscosity | Blow-up time | Prandtl's equations | EXISTENCE | MATHEMATICS, APPLIED | INCOMPRESSIBLE EULER EQUATIONS | PHYSICS, MULTIDISCIPLINARY | ZERO VISCOSITY LIMIT | PHYSICS, MATHEMATICAL | FLOW | BOUNDARY-LAYER EQUATIONS | ANALYTIC SOLUTIONS | UNSTEADY SEPARATION | HALF-SPACE | NAVIER-STOKES SOLUTIONS

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

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 7, pp. 3942 - 3972

We consider stationary axisymmetric solutions of the Euler–Poisson equations, which govern the internal structure of barotropic gaseous stars...

Nonlinear integral equation | Euler–Poisson equations | Axisymmetric solutions | Free boundary | Stellar rotation | EXISTENCE | MATHEMATICS | Euler-Poisson equations | STARS | Mathematics - Analysis of PDEs

Nonlinear integral equation | Euler–Poisson equations | Axisymmetric solutions | Free boundary | Stellar rotation | EXISTENCE | MATHEMATICS | Euler-Poisson equations | STARS | Mathematics - Analysis of PDEs

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 03/2016, Volume 300, pp. 402 - 426

A new finite element method for solving the Euler equations in Lagrangian coordinates is proposed...

Finite element method | Conservation equations | Parabolic regularization | Entropy–viscosity | Lagrangian hydrodynamics | Entropy-viscosity | HYDRODYNAMICS | ARTIFICIAL VISCOSITY | SCHEME | GAS-DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONSERVATION | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | SYSTEMS | Analysis | Air forces | Methods | Fluid dynamics | Viscosity | Stabilization | Mathematical analysis | Mathematical models | Entropy | Euler equations | Diffusion

Finite element method | Conservation equations | Parabolic regularization | Entropy–viscosity | Lagrangian hydrodynamics | Entropy-viscosity | HYDRODYNAMICS | ARTIFICIAL VISCOSITY | SCHEME | GAS-DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONSERVATION | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | SYSTEMS | Analysis | Air forces | Methods | Fluid dynamics | Viscosity | Stabilization | Mathematical analysis | Mathematical models | Entropy | Euler equations | Diffusion

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

International journal of non-linear mechanics, ISSN 0020-7462, 11/2016, Volume 86, pp. 185 - 195

The observation that the hyperbolic shallow water equations and the Green–Naghdi equations in Lagrangian coordinates have the form of an Euler...

Green–Naghdi model | Lie group | Noether's theorem | Hyperbolic shallow water equations | Invariant solution | MECHANICS | Green-Naghdi model | Environmental law | Analysis

Green–Naghdi model | Lie group | Noether's theorem | Hyperbolic shallow water equations | Invariant solution | MECHANICS | Green-Naghdi model | Environmental law | Analysis

Journal Article