A Regularity Result for the Incompressible Elastodynamics with a Free Interface

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 H³, we are able to establish the regularity in space $H^{2.5+\delta}$. 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.

Keywords

Free boundary / incompressible elastodynamics equations / a priori estimates