We study the solvability in anisotropic Besov spaces , σ ∈ ℝ₊, p,q ∈ (1,∞) of an initial-boundary value problem for the linear parabolic system which arises in the study of the compressible Navier-Stokes system with boundary slip conditions. The proof of existence of a unique solution in is divided into three steps: 1° First the existence of solutions to the problem with vanishing initial conditions is proved by applying the Paley-Littlewood decomposition and some ideas of Triebel. All considerations in this step are performed on the Fourier transform of the solution. 2° Applying the regularizer technique the existence is proved in a bounded domain. 3° The problem with nonvanishing initial data is solved by an appropriate extension of initial data.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-36,
author = {Ewa Zadrzy\'nska and Wojciech M. Zaj\k aczkowski},
title = {Some linear parabolic system in Besov spaces},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {567-612},
zbl = {1173.35067},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-36}
}
Ewa Zadrzyńska; Wojciech M. Zajączkowski. Some linear parabolic system in Besov spaces. Banach Center Publications, Tome 83 (2008) pp. 567-612. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-36/