Decay of Dissipative Equations and Negative Sobolev Spaces

• Published in: Communications in partial differential equations Vol. 37; no. 12; pp. 2165 - 2208
• Main Authors: Guo, Yan, Wang, Yanjin
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.01.2012; Taylor & Francis Ltd
• Subjects: Aerodynamics; Boltzmann equation; Decay; Decay rate; Derivatives; Dissipation; Energy method; Eulers equations; Mathematical analysis; Navier-Stokes equations; Negative Sobolev space; Optimal decay rates; Optimization; Partial differential equations; Sobolev interpolation

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...