Convergence rates of solutions to the compressible Hookean elastodynamics

In this paper, we consider the low Mach number limit of the compressible Hookean elastodynamics in a bounded domain. Based on previous uniform existence and convergence results, we further study the convergence rates of the solutions. By combining time-average method and the energy estimates, we show that, as the Mach number ϵ goes to zero, the solutions of the compressible Hookean elastodynamics will converge to the solution of the limit system at the rate of O(ϵ ) when the initial data are ill-prepared. If the initial data are assumed to be well-prepared, the convergence rates can be improved to O(ϵ ^2) .