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Indexed by:期刊论文

Date of Publication:2018-09-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE

Volume:465

Issue:2

Page Number:1075-1093

ISSN No.:0022-247X

Key Words:Incompressible fluid; Korteweg type; Strong solutions; Vacuum; Cauchy problem

Abstract: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.