Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

被引:13
作者
Lin, Yu-Chu [1 ]
Wang, Haitao [2 ,3 ]
Wu, Kung-Chien [1 ,4 ]
机构
[1] Natl Cheng Kung Univ, Dept Math, Tainan, Taiwan
[2] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai, Peoples R China
[3] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China
[4] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei, Taiwan
关键词
Boltzmann equation; Fluid-like wave; Kinetic-like wave; Maxwellian states; Mixture Lemma; Singular wave; Pointwise estimate; LARGE-TIME BEHAVIOR; GREENS-FUNCTION; POTENTIALS; DECAY; SPACE;
D O I
10.1007/s10955-018-2047-4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
引用
收藏
页码:927 / 964
页数:38
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