Local existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Li, Jinkai¹ 

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Local existence and uniqueness;    Density-dependent incompressible Navier Stokes equations;    Compatibility condition;    Gronwall type inequality;   

DOI  :  10.1016/j.jde.2017.07.021

来源: Elsevier

【 摘 要 】

In this paper, we consider the initial-boundary value problem to the nonhomogeneous incompressible Navier Stokes equations. Local strong solutions are established, for any initial data (rho(0), u(0)) is an element of (W-1,W-gamma boolean AND L-infinity) x H-0,sigma(1), with gamma > 1, and if gamma >= 2, then the strong solution is unique. The initial density is allowed to be nonnegative, and in particular, the initial vacuum is allowed. The assumption on the initial data is weaker than the previous widely used one that (rho(0), u(0)) is an element of (H-1 boolean AND L-infinity) x (H-0,sigma(1) boolean AND H-2), and no compatibility condition is required. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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