The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of th...The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space R^3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J.,Global solutions to the Boltzmann equation with external forces, Anal. Appl.(Singap.), 3,2005, 157–193], no smallness condition on the Sobolev norm H^1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L^2-L~∞ estimates.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(No.NS2012122)
文摘The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space R^3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J.,Global solutions to the Boltzmann equation with external forces, Anal. Appl.(Singap.), 3,2005, 157–193], no smallness condition on the Sobolev norm H^1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L^2-L~∞ estimates.
