Vanishing viscosity in the plane for vorticity in borderline spaces of Besov type

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:235

Article

Cozzi, Elaine ; Kelliher, James R.

关键词: fluid mechanics;    vanishing viscosity;    Euler equations;   

DOI  :  10.1016/j.jde.2006.12.022

来源: Elsevier

【 摘 要 】

The existence and uniqueness of solutions to the Euler equations for initial vorticity in B-Gamma boolean AND L-P0 boolean AND L-P1 was proved by Misha Vishik, where B-Gamma is a borderline Besov space parameterized by the function Gamma and 1 < p(0) < 2 < p(1). Vishik established short time existence and uniqueness when Gamma(n) = O(log n) and global existence and uniqueness when Gamma(n) = O (log 1/2 n). For initial vorticity in B-Gamma boolean AND L-2, we establish the vanishing viscosity limit in L-2(R-2) of solutions of the Navier-Stokes equations to a solution of the Euler equations in the plane, convergence being uniform over short time when Gamma(n) = O (log n) and uniform over any finite time when Gamma(n) = O (log(kappa) n), 0 <= kappa < 1, and we give a bound on the rate of convergence. This allows us to extend the class of initial vorticities for which both global existence and uniqueness of solutions to the Euler equations can be established to include B-Gamma boolean AND L-2 when Gamma(n) = O (log(kappa) n) for 0 < kappa < 1.(c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free