Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Gu, Xumin¹  Wang, Fan² 

[1] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China

[2] Southwest Jiaotong Univ, Dept Math, Chengdu 610031, Sichuan, Peoples R China

关键词: Free boundary;    Well-posedness;    Elastodynamics;    Inviscid flows;    Incompressible fluids;   

DOI  :  10.1016/j.jmaa.2019.123529

来源: Elsevier

【 摘 要 】

We consider the free boundary problem for the flow of an incompressible inviscid elastic fluid. The columns of the deformation gradient are tangent and the pressure vanishes along the free interface. We prove the local existence of a unique smooth solution to the free boundary problem under the mixed type stability condition, provided that the Rayleigh-Taylor sign condition is satisfied at all the points of the initial interface where the non-collinearity condition for the deformation gradient (among three columns of the deformation gradient there are two non-collinear vectors) fails. In particular, we solve an open problem proposed by Y. Trakhinin in the paper [29] under the incompressible setting. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free