Global existence for the Boltzmann equation in $ L^r_v L^\infty_t L^\infty_x $ spaces

Koya Nishimura

doi:10.3934/cpaa.2019083

Article Contents

2019, Volume 18, Issue 4: 1769-1782. Doi: 10.3934/cpaa.2019083

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Global existence for the Boltzmann equation in $ L^r_v L^\infty_t L^\infty_x $ spaces

Koya Nishimura

Independent scholar

Received: June 2018

Revised: June 2018

Published: January 2019

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Abstract

We study the Boltzmann equation near a global Maxwellian. We prove the global existence of a unique mild solution with initial data which belong to the $ L^r_v L^\infty_x $ spaces where $ r \in (1,\infty] $ by using the excess conservation laws and entropy inequality introduced in [5].

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Mathematics Subject Classification: Primary: 35Q20, 35A01; Secondary: 82B40.

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References

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