Time decay of solutions for generalized Boussinesq equations in two space dimensions
The Cauchy problem for the two-dimensional generalized Boussinesq equations is considered. Local existence theorems are proved in two Sobolev spaces, with one of them being weighted. Through the Fourier transform, the system is reduced to integral equations and the contraction mapping argument is used. The study of decay in the supremum norm is first done for the linearized system. Then the same law of decay is established for the nonlinear system under the assumptions that initial data are small and \(p>6\) in the nonlinear term \(n^p n_{x}\).
scientific article; zbMATH DE number 1348142