Periodic solutions for the Blackstock-Crighton-Westervelt equation

Abstract

We investigate the Blackstock-Crighton-Westervelt equation which models nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We prove exis- tence and regularity, in a Lp −Lq setting, of time-periodic solutions for a given sufficiently small time-periodic forcing data, and homogeneous Dirichlet boundary conditions over a cylindrical domain. We show maximal Lp-regularity for the abstract linearized model. We use techniques of operator-valued Fourier multiplier theorems combined with a gen- eralized version of the implicit function theorem.