The optimal decay rate of strong solution for the compressible Navier-Stokes equations with large initial data

PHYSICA D-NONLINEAR PHENOMENA

卷:406

Article

Gao, Jincheng¹  Wei, Zhengzhen¹  Yao, Zheng-an¹ 

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

关键词: Compressible Navier-Stokes equations;    Optimal decay rate;    Large initial data;   

DOI  :  10.1016/j.physd.2020.132506

来源: Elsevier

【 摘 要 】

In a recent paper (He et al., 2019), it is shown that the upper decay rate of global solution of compressible Navier-Stokes(CNS) equations converging to constant equilibrium state (1, 0) in H-1-norm is (1 + t)(- 34 (2p-1)) when the initial data is large and belongs to H-2(R-3) boolean AND L-p(R-3)(p epsilon [1, 2)). Thus, the first result in this paper is devoted to showing that the upper decay rate of the first order spatial derivative converging to zero in H-1-norm is (1+ t)(- 3/2 (1p - 12)-12.) For the case of p = 1, the lower bound of decay rate for the global solution of CNS equations converging to constant equilibrium state (1, 0) in L-2-norm is (1+ t)(-3/)4 if the initial data satisfies some low frequency assumption additionally. In other words, the optimal decay rate for the global solution of CNS equations converging to constant equilibrium state in L-2-norm is (1 + t)(- 3/4) although the associated initial data is large. (C) 2020 Elsevier B.V. All rights reserved.

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