Decay of Dissipative Equations and Negative Sobolev Spaces
By Yan Guo, Yanjin Wang. 2011
380 citations recorded by the source corpus.
We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1594650785b26da61a855280025a62bd1a7fe3dc
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- Decay of the Navier-Stokes-Poisson equations (2011, methodology): “This is an improvement of [9] where we required the smallness of the H [ N 2 ]+2 norm of initial data.”