TY - JOUR
T1 - Self-generating lower bounds and continuation for the Boltzmann equation
AU - Henderson, Christopher
AU - Snelson, Stanley
AU - Tarfulea, Andrei
N1 - Funding Information:
CH was partially supported by NSF Grant DMS-2003110. SS was partially supported by a Ralph E. Powe Award from ORAU. AT was partially supported by NSF Grant DMS-1816643.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space Rx3, 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.
AB - For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space Rx3, 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.
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U2 - 10.1007/s00526-020-01856-9
DO - 10.1007/s00526-020-01856-9
M3 - Article
AN - SCOPUS:85092588153
VL - 59
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 6
M1 - 191
ER -