Periodic Solutions For The Blackstock-Crighton-Westervelt Equation

We investigate the Blackstock–Crighton–Westervelt equation which models nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We prove existence and regularity, in a L^p−L^q 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 L^p-regularity for the abstract linearized model. We use techniques of operator-valued Fourier multiplier theorems combined with a generalized version of the implicit function theorem.