Global existence of Cauchy problem for Boussinesq paradigm equation

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Abstract

In this paper we study the Cauchy problem for the Boussinesq paradigm equation uttΔuβ1Δutt+β2Δ2u=Δf(u), where f(u)=α|u|p. New functionals are introduced and their sign preserving properties under the flow of the equation are studied. The existence of a global weak solution with supercritical initial energy is proved. The explicit value of the critical energy constant is found.

Keywords

Boussinesq equation
Double dispersion equation
Global existence
Cauchy problem
Supercritical initial energy

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