TY - JOUR
T1 - C∞ Smoothing for Weak Solutions of the Inhomogeneous Landau Equation
AU - Henderson, Christopher
AU - Snelson, Stanley
N1 - Funding Information:
Both authors were partially supported by National Science Foundation Grant DMS-1246999. CH was partially supported by NSF grant DMS-1907853. SS was partially supported by a Ralph E. Powe Award from ORAU.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - We consider the spatially inhomogeneous Landau equation with initial data that is bounded by a Gaussian in the velocity variable. In the case of moderately soft potentials, we show that weak solutions immediately become smooth, and remain smooth as long as the mass, energy, and entropy densities remain under control. For very soft potentials, we obtain the same conclusion with the additional assumption that a sufficiently high moment of the solution in the velocity variable remains bounded. Our proof relies on the iteration of local Schauder-type estimates.
AB - We consider the spatially inhomogeneous Landau equation with initial data that is bounded by a Gaussian in the velocity variable. In the case of moderately soft potentials, we show that weak solutions immediately become smooth, and remain smooth as long as the mass, energy, and entropy densities remain under control. For very soft potentials, we obtain the same conclusion with the additional assumption that a sufficiently high moment of the solution in the velocity variable remains bounded. Our proof relies on the iteration of local Schauder-type estimates.
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U2 - 10.1007/s00205-019-01465-7
DO - 10.1007/s00205-019-01465-7
M3 - Article
AN - SCOPUS:85074858331
VL - 236
SP - 113
EP - 143
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -