On the global existence for the axisymmetric Euler equations [PDF]
arXiv, 2007 This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in some critical Besov ...
arxiv
Regularity of Leray-Hopf solutions to Navier-Stokes equations [PDF]
arXiv, 2007 Limit behaviors of blow up solutions for impressible Navier-Stokes equations are obtained.
arxiv
Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation [PDF]
, 2007 We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical ($\alpha< 1/2$) dissipation $(-\Delta)^\alpha$ : If a Leray-Hopf weak solution is H\"{o}lder continuous $\theta\in C^\delta({\mathbb R}^2)$ with $\delta>1-2\alpha$ on the time interval $[t_0, t]$, then it is actually a classical solution on $(t_0,t]
arxiv +1 more source
Existence and uniqueness of the global solution to the Navier-Stokes boundary problem [PDF]
arXiv, 2015 A proof is given of the global existence and uniqueness of a weak solution to Navier-Stokes boundary problem. The proof is short and essentially self-contained.
arxiv
Application of harmonic analysis techniques to regularity problems of dissipative equations [PDF]
arXiv, 2018 We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared to classical energy methods.
arxiv
Finite energy weak solution of 2d Boussinesq equation with diffusive temperature [PDF]
arXiv, 2019 We show the existence of finite kinetic energy solution with prescribed kinetic energy to the 2d Boussinesq equations with diffusive temperature on torus.
arxiv
Localized non blow-up criterion of the Beale-Kato-Majda type for the 3D Euler equations [PDF]
arXiv, 2017 We prove a localized non blow-up theorem of the Beale-Kato-Majda type for the solution of the 3D incompressible Euler equations.
arxiv
Global well-posedness for Euler-Boussinesq system with critical dissipation [PDF]
, 2009 In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.
arxiv +1 more source
Trapping regions and an ODE-type proof of the existence and uniqueness theorem for Navier-Stokes equations with periodic boundary conditions on the plane [PDF]
arXiv, 2001 Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boundary conditions on the plane.
arxiv
Note on the finite time singularities for the 3D Navier-Stokes equations [PDF]
arXiv, 2005 The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.
arxiv