TY - JOUR
T1 - Relativistic boltzmann equation
T2 - Large time behavior and finite speed of propagation
AU - Lin, Yu Chu
AU - Lyu, Ming Jiea
AU - Wu, Kung Chien
N1 - Funding Information:
\ast Received by the editors April 20, 2020; accepted for publication (in revised form) August 10, 2020; published electronically December 1, 2020. https://doi.org/10.1137/20M1332761 Funding: The work of the first author was supported by the Ministry of Science and Technology, Taiwan (MOST) grant 109-2115-M-006-004. The work of the third author was supported by the Ministry of Science and Technology, Taiwan (MOST) grant 109-2636-M-006-005 and the National Center for Theoretical Sciences. \dagger Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan (yuchu@mail.ncku.edu.tw, mingjiealyu@gmail.com). \ddagger Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan and National Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan (kungchienwu@gmail.com).
PY - 2020
Y1 - 2020
N2 - In this paper, we deal with the relativistic Boltzmann equation in the whole space R3x under the closed to equilibrium setting. We obtain the existence, uniqueness, and large time behavior of the solution without imposing any Sobolev regularity (both the spatial and velocity variables) on the initial data. Moreover, we recognize the finite speed of propagation of the solution, which reflects the difference, in essence, between the relativistic Boltzmann equation and the classical Boltzmann equation.
AB - In this paper, we deal with the relativistic Boltzmann equation in the whole space R3x under the closed to equilibrium setting. We obtain the existence, uniqueness, and large time behavior of the solution without imposing any Sobolev regularity (both the spatial and velocity variables) on the initial data. Moreover, we recognize the finite speed of propagation of the solution, which reflects the difference, in essence, between the relativistic Boltzmann equation and the classical Boltzmann equation.
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U2 - 10.1137/20M1332761
DO - 10.1137/20M1332761
M3 - Article
AN - SCOPUS:85098753916
VL - 52
SP - 5994
EP - 6032
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 6
ER -