A Regularity Result for the Incompressible Elastodynamics with a Free Interface
Year: 2025
Type: article
Abstract: We consider the incompressible inviscid elastodynamics equations with a free surface and establish the regularity of solutions for elastic system. Compared with the previous result on this free boundary problem [ Gu X and Wang F, Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition, J. Math. Anal. Appl., 2020, 482(1): 123529] in space $H^3,$ we are able to establish the regularity in space $H^{2.5+δ}.$ It is achieved by reformulating the system into the Lagrangian formulation, presenting the uniform estimates for the pressure, the tangential estimates for the system, as well as the divergence and curl estimates.
Source: Journal of Mathematical Study
Author: Binqiang Xie
Institution: Guangdong University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414256932