Self-generating lower bounds and continuation for the Boltzmann equation
For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space R x 3 , we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds depend only on the initial data and upper bounds for the mass and energy...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2020-12, Vol.59 (6), Article 191 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Henderson, Christopher Snelson, Stanley Tarfulea, Andrei |
| description | For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space
R
x
3
, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds depend only on the initial data and upper bounds for the mass and energy densities of the solution. As an application, we improve the weakest known continuation criterion for large-data solutions, by removing the assumptions of mass bounded below and entropy bounded above. |
| doi_str_mv | 10.1007/s00526-020-01856-9 |
| format | Article |
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R
x
3
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R
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R
x
3
, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds depend only on the initial data and upper bounds for the mass and energy densities of the solution. As an application, we improve the weakest known continuation criterion for large-data solutions, by removing the assumptions of mass bounded below and entropy bounded above.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-020-01856-9</doi></addata></record> |
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| ispartof | Calculus of variations and partial differential equations, 2020-12, Vol.59 (6), Article 191 |
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| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Analysis Boltzmann transport equation Calculus of Variations and Optimal Control Optimization Control Lower bounds Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Systems Theory Theoretical Upper bounds |
| title | Self-generating lower bounds and continuation for the Boltzmann equation |
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