We study the incompressible limit of the compressible nonisentropic Hookean elastodynamics with general initial data in the whole space [Formula: see text]. First, we obtain the uniform estimates of the solutions in [Formula: see text] 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.

The low Mach number limit of the nonisentropic compressible Hookean elastodynamic equations is rigorously proved with respect to well-prepared initial data. We introduce certain suitable seminorms to obtain the uniform estimate of solutions, for which the critical point is to cancel the higher order derivate terms caused by the coupling of velocity and deformation gradient.

No abstract