Incompressible limit of nonisentropic Hookean elastodynamics

Abstract

We study the incompressible limit of the compressible nonisentropic Hookean elastodynamics with general initial data in the whole space Rd(d=2,3). First, we obtain the uniform estimates of the solutions in Hs(Rd) for s > d/2 + 1 being even and the existence of classic solutions on a time interval independent of the Mach number. Then, we prove that the solutions converge to the incompressible elastodynamic equations as the Mach number tends to zero.