Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force
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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 ℝ3. 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.
KeywordsBoltzmann equation Large potential force Stability Entropy-energy inequality L2 − L∞ method
2000 MR Subject Classification76P05 82C40 35B35
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- Li, F.-C. and Yu, H.-J., Global existence of classical solutions to the Boltzmann equation with external force for hard potentials, Int. Math. Res. Not. IMRN, 2008, Art. ID rnn112, 22 pages.Google Scholar