Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force |
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Authors: | Xiuhui YANG |
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Institution: | 1.Department of Mathematics, College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing,China |
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Abstract: | 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 ?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 H1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L2 ? L∞ estimates. |
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Keywords: | Boltzmann equation Large potential force Stability Entropy-energy inequality $L^2-L^infty$ method |
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