Eternal solutions of the Boltzmann equation near travelling Maxwellians |
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Authors: | Jinbo Wei |
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Institution: | Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China |
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Abstract: | It is shown in this paper that the Cauchy problem of the Boltzmann equation, with a cut-off soft potential and an initial datum close to a travelling Maxwellian, has a unique positive eternal solution. This eternal solution is exponentially decreasing at infinity for all t∈(−∞,∞), consequently the moments of any order are finite. This result gives a negative answer to the conjecture of Villani in the spatially inhomogeneous case. |
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Keywords: | Boltzmann equation Eternal positive solution Kaniel-Shinbrot iteration |
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