| Abstract: |
| We are concerned with the Cauchy problem on the Boltzmann equation in the whole space. The goal is to study solutions near Maxwellians with the perturbation admitting a polynomial tail in large velocities. We obtain global-in-time bounded mild solutions near global Maxwellians and construct solutions up to any finite time around local Maxwellians whose fluid quantities are classical solutions to the corresponding compressible Euler system around constant states. The main difficulty to be overcome in case of the whole space is the polynomial time decay of solutions which is much slower than the exponential rate in contrast with the torus case. |
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