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Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 12/2017, Volume 19, Issue 4, pp. 709 - 724
Journal Article
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
Journal Article
by Yuan, BQ and Wei, CZ
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
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2017, Volume 263, Issue 12, pp. 8979 - 9002
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
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
Journal Article
by Bie, QY and Cui, HB and Wang, QR and Yao, ZA
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
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
Journal 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
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
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2019, Volume 232, Issue 1, pp. 197 - 263
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
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 02/2019, Volume 77, Issue 4, pp. 1082 - 1090
Journal Article
Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 6/2019, Volume 21, Issue 2, pp. 1 - 32
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
Journal Article
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
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
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
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
Journal Article
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