The semirelativistic Choquard equation with a local nonlinear term
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July 2019, 39(7): 4303-4329. doi: 10.3934/dcds.2019174
The Boltzmann equation with frictional force for very soft potentials in the whole space
Yingzhe Fan 1, and Yuanjie Lei 2,3,,
School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
* Corresponding author: Yuanjie Lei
Received November 2016 Published April 2019
Fund Project: The corresponding author is supported by NSFC grant No.11601169 and 11871335
We develop a general energy method for proving the optimal time decay rates of the higher-order spatial derivatives of solutions to the Boltzmann-type and Landau-type systems in the whole space, for both hard potentials and soft potentials. With the help of this method, we establish the global existence and temporal convergence rates of solution near a given global Maxwellian to the Cauchy problem on the Boltzmann equation with frictional force for very soft potentials i.e. $ -3<\gamma<-2 $.
Keywords: Boltzmann equation with frictional force, soft potentials, energy method, optimal time decay rates, global existence.
Mathematics Subject Classification: 82B40, 35A01, 35Q83.
Citation: Yingzhe Fan, Yuanjie Lei. The Boltzmann equation with frictional force for very soft potentials in the whole space. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4303-4329. doi: 10.3934/dcds.2019174
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Yingzhe Fan Yuanjie Lei