GLOBAL SOLUTION FOR THE SPATIALLY INHOMOGENEOUS NON-CUTOFF KAC EQUATION
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 4503-4562 |
| Journal / Publication | SIAM Journal on Mathematical Analysis |
| Volume | 50 |
| Issue number | 4 |
| Online published | 30 Aug 2018 |
| Publication status | Published - 2018 |
Link(s)
Abstract
This paper is concerned with the Cauchy problem on the one-dimensional inhomogeneous non-cutoff Kac equation. Based on the analysis on the linearized operator obtained in [N. Lerner, Y. Morimoto, K. Pravda-Starov, and C.-J. Xu, J. Funct. Anal., 269 (2015), pp. 459-535], we first prove the existence of a global solution to the equation around a global Maxwellian by combining two sets of macro-micro decomposition. Then by using the dissipative norm of the linearized operator in the fractional Hermite-Sobolev space and using the perturbation theory, the spectrum structure of the linearized Kac equation is given. Based on this, the optimal time decay estimate for the nonlinear Kac equation is obtained.
Research Area(s)
- non-cutoff Kac equation, global existence, large time behavior, LARGE-TIME BEHAVIOR, BOLTZMANN-EQUATION, WHOLE SPACE, ANGULAR CUTOFF, STRICT POSITIVITY, MAXWELLIAN GAS, EQUILIBRIUM, REGULARITY, PROPAGATION, INEQUALITY
Citation Format(s)
GLOBAL SOLUTION FOR THE SPATIALLY INHOMOGENEOUS NON-CUTOFF KAC EQUATION. / YANG, Tong; YU, Hongjun.
In: SIAM Journal on Mathematical Analysis, Vol. 50, No. 4, 2018, p. 4503-4562.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
