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Global existence for the Boltzmann equation in $ L^r_v L^\infty_t L^\infty_x $ spaces
Independent scholar |
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 [
References:
[1] |
R. Duan, F. Huang, Y. Wang and T. Yang,
Global well-posedness of the Boltzmann equation with large Amplitude initial data, Arch. Rational Mech. Anal., 225 (2017), 375-424.
doi: 10.1007/s00205-017-1107-2. |
[2] |
Robert T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[3] |
Yan Guo,
The Vlasov-Poisson-Boltzmann system near Maxwellians, Comm. Pure Appl. Math., Vol. LV (2002), 1104-1135.
doi: 10.1002/cpa.10040. |
[4] |
Yan Guo,
Decay and continuity of Boltzmann equation in bounded domains, Arch. Rational Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[5] |
Yan Guo,
Bounded solutions for the Boltzmann equation, Quart. Appl. Math., LXVIII (2010), 143-148.
doi: 10.1090/S0033-569X-09-01180-4. |
[6] |
M. Strain Robert and Keya Zhu,
Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$, Kinetic and Related Models, 5 (2012), 383-415.
doi: 10.3934/krm.2012.5.383. |
[7] |
S. Ukai and T. Yang,
The Boltzmann equation in the space $L^2 \cap L^\infty_\beta$: Global and time-periodic solutions, Analysis and Applications, 4 (2006), 263-310.
doi: 10.1142/S0219530506000784. |
show all references
References:
[1] |
R. Duan, F. Huang, Y. Wang and T. Yang,
Global well-posedness of the Boltzmann equation with large Amplitude initial data, Arch. Rational Mech. Anal., 225 (2017), 375-424.
doi: 10.1007/s00205-017-1107-2. |
[2] |
Robert T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[3] |
Yan Guo,
The Vlasov-Poisson-Boltzmann system near Maxwellians, Comm. Pure Appl. Math., Vol. LV (2002), 1104-1135.
doi: 10.1002/cpa.10040. |
[4] |
Yan Guo,
Decay and continuity of Boltzmann equation in bounded domains, Arch. Rational Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[5] |
Yan Guo,
Bounded solutions for the Boltzmann equation, Quart. Appl. Math., LXVIII (2010), 143-148.
doi: 10.1090/S0033-569X-09-01180-4. |
[6] |
M. Strain Robert and Keya Zhu,
Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$, Kinetic and Related Models, 5 (2012), 383-415.
doi: 10.3934/krm.2012.5.383. |
[7] |
S. Ukai and T. Yang,
The Boltzmann equation in the space $L^2 \cap L^\infty_\beta$: Global and time-periodic solutions, Analysis and Applications, 4 (2006), 263-310.
doi: 10.1142/S0219530506000784. |
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