Gevrey regularity for Navier–Stokes equations under Lions boundary conditions (original) (raw)

Geometric regularity criteria for incompressible Navier–Stokes equations with Navier boundary conditions

Nonlinear Analysis

We study the regularity criteria for weak solutions to the 3D incompressible Navier-Stokes equations in terms of the direction of vorticity, taking into account the boundary conditions. A boundary regularity theorem is proved on regular curvilinear domains with a family of oblique derivative boundary conditions, provided that the directions of vorticity are coherently aligned up to the boundary. As an application, we establish the boundary regularity for weak solutions to Navier-Stokes equations in round balls, half-spaces and right circular cylindrical ducts, subject to the classical Navier and kinematic boundary conditions.

Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain

Communications in Mathematical Physics, 1987

In this note, we prove two regularity theorems for solutions to the Navier-Stokes equations of an I.B.V.P. in exterior domains. Namely, we prove that the setS of the singular points of a solution, if not empty, has at most 1-Hausdorff measureH 1(S)=0. Moreover, the setS is enclosed in a sphere of rayR for anyt>0. These results are obtained as corollaries to the partial regularity results furnished in [2].

Regularity criteria for the three-dimensional Navier-Stokes equations

Indiana University Mathematics Journal, 2008

In this paper we consider the three-dimensional Navier-Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one component of the velocity field, or alternatively in terms of one component of the pressure gradient, for the regularity of strong solutions to the three-dimensional Navier-Stokes equations.

Conditions Implying Regularity of the Three Dimensional Navier-Stokes Equation

Applications of Mathematics, 2005

We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.

Local regularity of the Navier–Stokes equations near the curved boundary

Journal of Mathematical Analysis and Applications, 2010

We present some regularity conditions for suitable weak solutions of the Navier-Stokes equations near the curved boundary of a sufficiently smooth domain. Our extend the work that was results established near a flat boundary by Gustafson, Kang and Tsai (2006) [6].