Existence and uniqueness of a solution to the Cauchy problem for the damped Boussinesq equation. (English) Zbl 0847.35111

Summary: We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time \(t\) and space coordinates for \(t> 0\) on a bounded time interval.


35Q35 PDEs in connection with fluid mechanics
76D33 Waves for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
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