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论文类型：期刊论文

发表时间：2018-09-15

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE

卷号：465

期号：2

页面范围：1075-1093

ISSN号：0022-247X

关键字：Incompressible fluid; Korteweg type; Strong solutions; Vacuum; Cauchy problem

摘要：This paper studies the local existence of strong solutions to the Cauchy problem of the incompressible fluid models of Korteweg type with vacuum as far field density. The corresponding 3D problem has been solved by Tan and Wang (2010) [21]. Notice that the technique used by Tan and Wang fails treating the 2D case, because the L-P-norm (p > 2) of the velocity u cannot be controlled in terms only of root pu and del u here. In the present paper, we will use the framework of weighted approximation estimates introduced by Liang (2015) [14] for Navier-Stokes equations to obtain the local existence of strong solutions provided the initial density does not decay very slowly at infinity, with the compact support case included. (C) 2018 Elsevier Inc. All rights reserved.