2006 / March Volume 1 No.1
Green's Function of Boltzmann Equation, 3-D Waves
| Published Date |
2006 / March
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| Title | Green's Function of Boltzmann Equation, 3-D Waves |
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| Pagination | 1-78 |
| Abstract | We study the Green's function for the linearized Boltzmann equation. For the short-time period, the Green's function
is dominated by the particle-like waves; and for large-time, by the fluid-like waves exhibiting the weak Huygens principle. The
fluid-like waves are constructed by the spectral analysis and complex analytic techniques, making uses of the rotational symmetry of the equation in the space variables. The particle-like waves are constructed by a Picard iteration, making uses of the exchange of regularity in the microscopic velocity with the regularity in the space variables through a Mixture Lemma. We obtain the pointwise estimates in the space and time variables of the Green's function through a long-short waves and particle-wave decompositions.
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| AMS Subject Classification |
76P05, 35L65, 82C40
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| Received |
2005-12-01
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