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Abstract In this paper, we consider the limit behavior of solutions to the Cauchy problem for damped Boussinesq equation in the regime of small viscosity in R n . It… Click to show full abstract
Abstract In this paper, we consider the limit behavior of solutions to the Cauchy problem for damped Boussinesq equation in the regime of small viscosity in R n . It is shown that the strong solutions of damped Boussinesq equation converge to a strong solution of Boussinesq equation in any time interval [ 0 , T ] . The key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped Boussinesq equation, which is a kind of new view. We analyze the dispersion by the techniques of high-low frequency decomposition and Littlewood-Paley dyadic decomposition, stationary phase estimate and some properties of Bessel function.
Journal Title: Journal of Differential Equations
Year Published: 2019
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