A Regularity Result for the Incompressible Elastodynamics with a Free Interface (Journal of Mathematical Study, 2025)
We consider the incompressible inviscid elastodynamics equations with afree surface and establish the regularity of solutions for elastic system. Compared withthe previous result on this free boundary problem [ Gu X and Wang F, Well-posednessof the free boundary problem in incompressible elastodynamics under the mixed typestability condition, J. Math. Anal. Appl., 2020, 482(1): 123529] in space $H^3,$ we are ableto establish the regularity in space $H^{2.5+δ}.$ It is achieved by reformulating the systeminto the Lagrangian formulation, presenting the uniform estimates for the pressure,the tangential estimates for the system, as well as the divergence and curl estimates.