New
Function Spaces for the Boltzmann Equation
Professor
Tong YANG
Department of Mathematics
We present some well-posedness theories for the Cauchy problem of the Boltzmann equation in some new function spaces. For the case
without external force, a new well-posedness theory
is obtained for solutions near an absolute Maxwellian
in a mild sense without any regularity assumptions. The optimal convergence
rates to the equilibrium in various spaces are also given together with the
spatial derivatives where no smallness assumptions are imposed on the
derivatives of the initial data. For the case with external force, the solution
operator is no longer a semi-group so that the analysis becomes complicated.
The well-posedness is shown in some Sobolev spaces and the optimal convergence rates are also derived.
This kind of research is closely related to the hypercoercivity
theory of the Boltzmann equation and has application
in the study of other physical problems, such as the time-periodic solutions in
the generation and propagation of sound waves.
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Date: |
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Time: |
4:00 – 5:00pm |
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Place: |
Room 517, Meng Wah Complex, HKU |
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All are welcome |
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