On the asymptotic behavior of solution for the generalized IBq equation with hydrodynamical damped term

By Shubin Wang, Huiyang Xu. 2012

50 citations recorded by the source corpus.

Abstract We study the Cauchy problem for the generalized IBq equation with hydrodynamical damped term in n -dimensional space. We observe that the dissipative structure of the linearized equation is of the regularity-loss type. This means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data. Under smallness condition on the initial data, we prove the global existence and decay of the small amplitude solution in the Sobolev space.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d308152261251bad8e1bb001ec29428ff53d7831