TY - JOUR
T1 - A Regularity Result for the Incompressible Elastodynamics with a Free Interface
AU - Xie , Binqiang
JO - Journal of Mathematical Study
VL - 3
SP - 338
EP - 361
PY - 2025
DA - 2025/09
SN - 58
DO - http://doi.org/10.4208/jms.v58n3.25.06
UR - https://global-sci.org/intro/article_detail/jms/24412.html
KW - Free boundary, incompressible elastodynamics equations, a priori estimates.
AB - <p style="text-align: justify;">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.</p>