Please use this identifier to cite or link to this item:
|Title:||Nonlinear wave propagations over a Boltzmann shock profile|
|Citation:||Yu, S.-H. (2010-10). Nonlinear wave propagations over a Boltzmann shock profile. Journal of the American Mathematical Society 23 (4) : 1041-1118. ScholarBank@NUS Repository. https://doi.org/10.1090/S0894-0347-2010-00671-6|
|Abstract:||In this paper we study the wave propagation over a Boltzmann shock profile and obtain pointwise time-asymptotic stability of Boltzmann shocks. We design a T-C scheme to study the coupling of the transverse and compression waves. The pointwise information of the Green's functions of the Boltzmann equation linearized around the end Maxwellian states of the Shock wave provides the basic estimates for the transient waves. The compression of the Boltzmann shock profile together with a low order damping allows for an accurate energy estimate by a localized scalar equation. These two methods are combined to construct an exponentially sharp pointwise linear wave propagation structure around a Boltzmann shock profile. The pointwise estimates thus obtained are strong enough to study the pointwise nonlinear wave coupling and to conclude the convergence with an optimal convergent rate O(1)[(1 +t)(l + εt)]-1/2 around the Boltzmann shock front, where ε is the strength of a shock wave. © 2010 American Mathematical Society.|
|Source Title:||Journal of the American Mathematical Society|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Mar 26, 2019
WEB OF SCIENCETM
checked on Mar 18, 2019
checked on Mar 1, 2019
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.