Existence of non‐resonant solutions of time‐periodic type is established for the Kuznetsov equation with a periodic forcing term. The equation is considered in a three‐dimensional whole‐space, half‐space and bounded domain, and with both non‐homogeneous Dirichlet and Neumann boundary values. A method based on Lp estimates for the corresponding linearization, namely the wave equation with Kelvin‐Voigt damping, is employed.

The Blackstock-Crighton equations describe the motion of a viscous, heatconducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into account. In this article, a mathematical analysis of the Blackstock-Crighton equations with a time-periodic forcing term is carried out. For arbitrary time-periodic data (sufficiently restricted in size) it is shown that a time-periodic solution of the same period always exists. This implies that the dissipative effects are sufficient to avoid resonance within the Blackstock-Crighton models. The equations are considered in a threedimensional bounded domain with both non-homogeneous Dirichlet and Neumann boundary values. Existence of a solution is obtained via a fixed-point argument based on appropriate a priori estimates for the linearized equations.MSC2010: Primary 35Q35, 76N10, 76D33, 35B10, 35B34.

The time‐periodic Stokes problem in a half‐space with fully inhomogeneous right‐hand side is investigated. Maximal regularity in a time‐periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a decomposition of the solution into a steady‐state and a purely oscillatory part in order to identify the suitable function spaces.

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