Regularity criteria in weak spaces for Navier-Stokes equations in R3 [PDF]
arXiv, 2006 In this paper we establish a Serrin type regularity criterion on the gradient of pressure in weak spaces for the Leray-Hopf weak solutions of the Navier-Stokes equations in R3.
arxiv
Global regularity for the 3D Navier-Stokes and the 3D Euler equations [PDF]
arXiv, 2007 The article `Global regularity for the 3D Navier-Stokes and the 3D Euler equations'(arXiv:0711.2453) is withdrawn due to a serious error in the proof.
arxiv
On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations [PDF]
arXiv, 2007 We prove new \emph{a priori} estimates for the 3D Euler, the 3D Navier-Stokes and the 2D quasi-geostrophic equations by the method of similarity transforms.
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
Hydrodynamics, probability and the geometry of the diffeomorphisms group [PDF]
arXiv, 2008 We characterize the solution of Navier-Stokes equation as a stochastic geodesic on the diffeomorphisms group, thus generalizing Arnold's description of the Euler flow.
arxiv
Inertial forces in the Navier-Stokes equation [PDF]
arXiv, 2011 We estimate the inertial force field in the 3d Euler/Navier-Stokes equation in function of |u|_\infty and |\nabla u |_\infty and provide an application to the well-posed ...
arxiv
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
A Liouville Type Theorem for Steady-State Navier-Stokes Equations [PDF]
arXiv, 2016 A Liouville type theorem is proven for the steady-state Navier-Stokes equations. It follows from the corresponding theorem on the Stokes equations with the drift. The drift is supposed to belong to a certain Morrey space.
arxiv
Some examples of singular fluid flows [PDF]
arXiv, 2001 We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg. By means of a partial regularity theorem (proved elsewhere), it turns out that we are able to show the existence of a suitable weak solution to the Navier-Stokes equations with a singular set of ...
arxiv
Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise [PDF]
arXiv, 2002 We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential.
arxiv