Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 12/2017, Volume 19, Issue 4, pp. 709 - 724

The energy dissipation of the Navier–Stokes equations is controlled by the viscous force defined by the Laplacian $$-\Delta $$ - Δ , while that of the...

Generalized Navier–Stokes equations | Mathematical Methods in Physics | Fluid- and Aerodynamics | 35B35 | well-posedness | Classical and Continuum Physics | 35Q35 | 35B32 | 86A10 | analytic semigroup | Physics | Besov spaces | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | QUASI-GEOSTROPHIC EQUATION | GEVREY REGULARITY | ATMOSPHERE | Generalized Navier-Stokes equations

Generalized Navier–Stokes equations | Mathematical Methods in Physics | Fluid- and Aerodynamics | 35B35 | well-posedness | Classical and Continuum Physics | 35Q35 | 35B32 | 86A10 | analytic semigroup | Physics | Besov spaces | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | QUASI-GEOSTROPHIC EQUATION | GEVREY REGULARITY | ATMOSPHERE | Generalized Navier-Stokes equations

Journal Article

2.
Full Text
On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 73, Issue 7, pp. 2334 - 2341

This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. When the velocity field satisfies for , then...

Micropolar fluid flows | Regularity criterion | Besov spaces | MATHEMATICS | MAGNETO-HYDRODYNAMICS EQUATIONS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | WEAK SOLUTIONS | Mathematical analysis | Micropolar fluids | Fourier analysis | Nonlinearity | Criteria | Localization | Regularity | Three dimensional

Micropolar fluid flows | Regularity criterion | Besov spaces | MATHEMATICS | MAGNETO-HYDRODYNAMICS EQUATIONS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | WEAK SOLUTIONS | Mathematical analysis | Micropolar fluids | Fourier analysis | Nonlinearity | Criteria | Localization | Regularity | Three dimensional

Journal Article

3.
BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, ISSN 2008-1898, 2017, Volume 10, Issue 6, pp. 3030 - 3037

In this paper, we investigate the blow-up criterion of a smooth solution of the nematic liquid crystal flow in three-dimensional space. More precisely, We...

EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | HARMONIC MAPS | blow-up criteria | WELL-POSEDNESS | Besov space | MATHEMATICS | Nematic liquid crystal flow | regularity criteria | NAVIER-STOKES EQUATIONS | BLOW-UP | HEAT-FLOW

EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | HARMONIC MAPS | blow-up criteria | WELL-POSEDNESS | Besov space | MATHEMATICS | Nematic liquid crystal flow | regularity criteria | NAVIER-STOKES EQUATIONS | BLOW-UP | HEAT-FLOW

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 12/2017, Volume 263, Issue 12, pp. 8979 - 9002

We investigate the existence, uniqueness and stability of bounded and almost periodic mild solutions to several Navier–Stokes flow problems. In our strategy,...

Almost periodicity | Stokes operator | Navier–Stokes flows in Besov Spaces | Oseen operator | Bounded solutions and stability | Navier–Stokes–Oseen equations | APERTURE DOMAIN | EXISTENCE | Navier-Stokes flows in Besov Spaces | ROTATING OBSTACLE | WHOLE SPACE | BESOV-SPACES | EQUATIONS | ILL-POSEDNESS | NONSTATIONARY STOKES | MATHEMATICS | OPERATOR | Navier-Stokes-Oseen equations | PERTURBED HALF-SPACE | Fluid dynamics

Almost periodicity | Stokes operator | Navier–Stokes flows in Besov Spaces | Oseen operator | Bounded solutions and stability | Navier–Stokes–Oseen equations | APERTURE DOMAIN | EXISTENCE | Navier-Stokes flows in Besov Spaces | ROTATING OBSTACLE | WHOLE SPACE | BESOV-SPACES | EQUATIONS | ILL-POSEDNESS | NONSTATIONARY STOKES | MATHEMATICS | OPERATOR | Navier-Stokes-Oseen equations | PERTURBED HALF-SPACE | Fluid dynamics

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 8/2008, Volume 189, Issue 2, pp. 283 - 300

We establish two new estimates for a transport-diffusion equation. As an application we treat the problem of global persistence of the Besov regularity...

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES SYSTEM | EULER EQUATIONS | Studies | Analysis of PDEs | Mathematics

Mechanics | Fluids | Mathematical and Computational Physics | Physics | Electromagnetism, Optics and Lasers | Complexity | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES SYSTEM | EULER EQUATIONS | Studies | Analysis of PDEs | Mathematics

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 16, pp. 6589 - 6603

In this paper, we investigate large time behavior of global‐in‐time strong solution to the three‐dimensional compressible flow of nematic liquid crystal with...

energy estimates | temporal decay estimates | compressible nematic liquid crystal flow | Besov space | SYSTEM | TATARU SOLUTIONS | MATHEMATICS, APPLIED | ENERGY | LARGE-TIME BEHAVIOR | KOCH | NANOFLUID | NAVIER-STOKES EQUATIONS | REGULARITY | WEAK SOLUTIONS | ONSET | Thermodynamics | Interpolation | Decay rate | Function space | Norms | Nematic crystals | Liquid crystals | Compressible flow | Cauchy problem

energy estimates | temporal decay estimates | compressible nematic liquid crystal flow | Besov space | SYSTEM | TATARU SOLUTIONS | MATHEMATICS, APPLIED | ENERGY | LARGE-TIME BEHAVIOR | KOCH | NANOFLUID | NAVIER-STOKES EQUATIONS | REGULARITY | WEAK SOLUTIONS | ONSET | Thermodynamics | Interpolation | Decay rate | Function space | Norms | Nematic crystals | Liquid crystals | Compressible flow | Cauchy problem

Journal Article

7.
Incompressible Limit for the Compressible Flow of Liquid Crystals in L-p Type Critical Besov Spaces

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 06/2018, Volume 38, Issue 6, pp. 2879 - 2910

The present paper is devoted to the compressible nematic liquid crystal flow in the whole space R-N (N >= 2). Here we concentrate on the incompressible limit...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | L-p type critical Besov spaces | global existence | incompressible limit | ENERGY | Liquid crystal flow | NAVIER-STOKES | EQUATIONS | MACH NUMBER LIMIT | WEAK SOLUTIONS

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | L-p type critical Besov spaces | global existence | incompressible limit | ENERGY | Liquid crystal flow | NAVIER-STOKES | EQUATIONS | MACH NUMBER LIMIT | WEAK SOLUTIONS

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2010, Volume 61, Issue 1, pp. 63 - 72

In this paper, we study the inviscid limit for the 3-D axisymmetric incompressible fluid flows without swirl and prove the convergence rate. We will also prove...

Engineering | Navier–Stokes equations | Mathematical Methods in Physics | Inviscid limit | 76C05 | 76D05 | Axisymmetric flows without swirl | 35Q30 | Euler equations | Theoretical and Applied Mechanics | Besov spaces | Navier-Stokes equations | EULER SYSTEM | MATHEMATICS, APPLIED | QUASI-GEOSTROPHIC EQUATION | NAVIER-STOKES SYSTEM

Engineering | Navier–Stokes equations | Mathematical Methods in Physics | Inviscid limit | 76C05 | 76D05 | Axisymmetric flows without swirl | 35Q30 | Euler equations | Theoretical and Applied Mechanics | Besov spaces | Navier-Stokes equations | EULER SYSTEM | MATHEMATICS, APPLIED | QUASI-GEOSTROPHIC EQUATION | NAVIER-STOKES SYSTEM

Journal Article

Journal of Technology & Science, ISSN 1944-1894, 11/2017, p. 657

Newspaper Article

Journal of Differential Equations, ISSN 0022-0396, 06/2015, Volume 258, Issue 12, pp. 4368 - 4397

In recent paper , Y. Du and K. Wang (2013) proved that the global-in-time Koch–Tataru type solution to the -dimensional incompressible nematic liquid crystal...

Nematic liquid crystal flow | Navier–Stokes equations | Littlewood–Paley decomposition | Trajectory | Regularity | Besov space | Littlewood-Paley decomposition | 7Nematic liquid crystal flow | Navier-Stokes equations | MATHEMATICS | WELL-POSEDNESS | WEAK SOLUTIONS | FLOW

Nematic liquid crystal flow | Navier–Stokes equations | Littlewood–Paley decomposition | Trajectory | Regularity | Besov space | Littlewood-Paley decomposition | 7Nematic liquid crystal flow | Navier-Stokes equations | MATHEMATICS | WELL-POSEDNESS | WEAK SOLUTIONS | FLOW

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 11/2019, Volume 234, Issue 2, pp. 911 - 923

We consider the stationary Navier–Stokes equations in $$\mathbb {R}^n$$ R n for $$n\geqq 3$$ n ≧ 3 in the scaling invariant Besov spaces. It is proved that if...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | Function space | Fluid dynamics | Mathematical analysis | Fluid flow | Scaling | Well posed problems | Invariants | Navier-Stokes equations | Convergence

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MATHEMATICS, APPLIED | MECHANICS | Function space | Fluid dynamics | Mathematical analysis | Fluid flow | Scaling | Well posed problems | Invariants | Navier-Stokes equations | Convergence

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2019, Volume 232, Issue 1, pp. 197 - 263

We introduce a notion of global weak solution to the Navier–Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | REGULARITY | STABILITY | NORMS | WELL-POSEDNESS | BLOW-UP | INITIAL DATA | SELF-SIMILAR SOLUTIONS | Bisphenol-A | Function space | Fluid dynamics | Initial conditions | Mathematical analysis | Fluid flow | Navier-Stokes equations | Self-similarity | Mathematics - Analysis of PDEs

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | REGULARITY | STABILITY | NORMS | WELL-POSEDNESS | BLOW-UP | INITIAL DATA | SELF-SIMILAR SOLUTIONS | Bisphenol-A | Function space | Fluid dynamics | Initial conditions | Mathematical analysis | Fluid flow | Navier-Stokes equations | Self-similarity | Mathematics - Analysis of PDEs

Journal Article

ISRAEL JOURNAL OF MATHEMATICS, ISSN 0021-2172, 06/2017, Volume 220, Issue 1, pp. 283 - 332

In this paper we consider Euler equations (E) for an incompressible ideal fluid filling the whole space a"e (n) for n ae 2. We prove local-in-time...

MATHEMATICS | INCOMPRESSIBLE PERFECT FLUID | NAVIER-STOKES EQUATIONS | BLOW-UP CRITERION | REGULARITY | HARDY-SPACES | WELL-POSEDNESS | TRIEBEL-LIZORKIN SPACES | LOCAL EXISTENCE | VORTICITY | SOBOLEV | Research | Mathematical research | Differential equations | Topological spaces

MATHEMATICS | INCOMPRESSIBLE PERFECT FLUID | NAVIER-STOKES EQUATIONS | BLOW-UP CRITERION | REGULARITY | HARDY-SPACES | WELL-POSEDNESS | TRIEBEL-LIZORKIN SPACES | LOCAL EXISTENCE | VORTICITY | SOBOLEV | Research | Mathematical research | Differential equations | Topological spaces

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2019, Volume 77, Issue 4, pp. 1082 - 1090

We study the Cauchy problem of the fractional Navier–Stokes equations in critical variable exponent Fourier–Besov spaces . We discuss some properties of...

Global well-posedness | Fractional Navier–Stokes equations | Variable exponent Fourier–Besov spaces | Variable exponent Fourier-Besov spaces | CORIOLIS-FORCE | MATHEMATICS, APPLIED | REGULARITY | LEBESGUE | ILL-POSEDNESS | Fractional Navier-Stokes equations | Function space | Fluid dynamics | Mathematical analysis | Fluid flow | Well posed problems | Navier-Stokes equations | Cauchy problem

Global well-posedness | Fractional Navier–Stokes equations | Variable exponent Fourier–Besov spaces | Variable exponent Fourier-Besov spaces | CORIOLIS-FORCE | MATHEMATICS, APPLIED | REGULARITY | LEBESGUE | ILL-POSEDNESS | Fractional Navier-Stokes equations | Function space | Fluid dynamics | Mathematical analysis | Fluid flow | Well posed problems | Navier-Stokes equations | Cauchy problem

Journal Article

Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 6/2019, Volume 21, Issue 2, pp. 1 - 32

We consider the compressible Navier–Stokes–Korteweg system describing the dynamics of a liquid–vapor mixture with diffuse interphase. The global solutions are...

Secondary 35Q35 | Mathematical Methods in Physics | time-decay | Fluid- and Aerodynamics | well-posedness | Classical and Continuum Physics | Compressible Navier–Stokes–Korteweg system | Physics | Besov space | Primary 42B37 | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | STABILITY | Compressible Navier-Stokes-Korteweg system

Secondary 35Q35 | Mathematical Methods in Physics | time-decay | Fluid- and Aerodynamics | well-posedness | Classical and Continuum Physics | Compressible Navier–Stokes–Korteweg system | Physics | Besov space | Primary 42B37 | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | STABILITY | Compressible Navier-Stokes-Korteweg system

Journal Article

Revista Matematica Iberoamericana, ISSN 0213-2230, 2015, Volume 31, Issue 4, pp. 1375 - 1402

We prove the ill-posedness of the 3-D baratropic Navier-Stokes equation for the initial density and velocity belonging to the critical Besov space (B-p,1(3/p)...

Ill-posedness | Besov space | Compressible Navier-Stokes equations | MATHEMATICS | WELL-POSEDNESS | GLOBAL EXISTENCE | Compressible Navier Stokes equations | ill-posedness

Ill-posedness | Besov space | Compressible Navier-Stokes equations | MATHEMATICS | WELL-POSEDNESS | GLOBAL EXISTENCE | Compressible Navier Stokes equations | ill-posedness

Journal Article

17.
Full Text
Ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space near BMO − 1

Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 258, Issue 10, pp. 3376 - 3387

The ill-posedness of the 3D-Navier–Stokes equations in a generalized Besov space which is smaller than ( ) is considered. In 2008, Bourgain–Pavlović proved...

Navier–Stokes equations | Ill-posedness | Besov spaces | Navier-Stokes equations | MATHEMATICS | MORREY SPACES

Navier–Stokes equations | Ill-posedness | Besov spaces | Navier-Stokes equations | MATHEMATICS | MORREY SPACES

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 06/2017, Volume 17, Issue 2, pp. 717 - 747

We consider the Cauchy problem of the compressible Navier-Stokes system coupled with a Poisson equation. We give the optimal well-posedness in terms of scaling...

Lagrangian coordinates | Compressible Navier–Stokes–Poisson system | Besov spaces | DENSITY | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | L-P-FRAMEWORK | Compressible Navier-Stokes-Poisson system | EQUATIONS | FLOW

Lagrangian coordinates | Compressible Navier–Stokes–Poisson system | Besov spaces | DENSITY | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | L-P-FRAMEWORK | Compressible Navier-Stokes-Poisson system | EQUATIONS | FLOW

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2017, Volume 68, Issue 1, pp. 1 - 37

In this paper, we study the global well posedness of the 3D incompressible magnetohydrodynamic system with horizontal dissipation and horizontal magnetic...

Engineering | Mathematical Methods in Physics | 35Q35 | 76D03 | Theoretical and Applied Mechanics | MHD system | Global strong solution | Besov spaces | DISSIPATION | MATHEMATICS, APPLIED | SINGULARITIES | HYDRODYNAMICS | WELL-POSEDNESS | NAVIER-STOKES EQUATIONS | REGULARITY | 2D MHD EQUATIONS | CRITERION | WEAK SOLUTIONS | WELLPOSEDNESS | Information science

Engineering | Mathematical Methods in Physics | 35Q35 | 76D03 | Theoretical and Applied Mechanics | MHD system | Global strong solution | Besov spaces | DISSIPATION | MATHEMATICS, APPLIED | SINGULARITIES | HYDRODYNAMICS | WELL-POSEDNESS | NAVIER-STOKES EQUATIONS | REGULARITY | 2D MHD EQUATIONS | CRITERION | WEAK SOLUTIONS | WELLPOSEDNESS | Information science

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 11/2016, Volume 30, Issue 28n29, p. 1640025

We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time...

Stochastic magnetohydrodynamcis equations | harmonic analysis | Besov spaces | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | NAVIER-STOKES EQUATIONS | NOISE | PHYSICS, MATHEMATICAL | TURBULENT FLOWS | ALPHA MODEL | Fluid dynamics

Stochastic magnetohydrodynamcis equations | harmonic analysis | Besov spaces | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | NAVIER-STOKES EQUATIONS | NOISE | PHYSICS, MATHEMATICAL | TURBULENT FLOWS | ALPHA MODEL | Fluid dynamics

Journal Article

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