Some linear parabolic system in Besov spaces

Ewa Zadrzyńska, and Wojciech M. Zajączkowski. "Some linear parabolic system in Besov spaces." Banach Center Publications 81.1 (2008): 567-612. <http://eudml.org/doc/281623>.

@article{EwaZadrzyńska2008,
abstract = {We study the solvability in anisotropic Besov spaces $B_\{p,q\}^\{σ/2,σ\}(Ω^T)$, 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 $B_\{p,q\}^\{σ/2 + 1,σ + 2\}(Ω^T)$ 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.},
author = {Ewa Zadrzyńska, Wojciech M. Zajączkowski},
journal = {Banach Center Publications},
keywords = {boundary slip conditions; Besov regularity of solutions; compressible Navier-Stokes systems; anisotropic Besov spaces},
language = {eng},
number = {1},
pages = {567-612},
title = {Some linear parabolic system in Besov spaces},
url = {http://eudml.org/doc/281623},
volume = {81},
year = {2008},
}

TY - JOUR
AU - Ewa Zadrzyńska
AU - Wojciech M. Zajączkowski
TI - Some linear parabolic system in Besov spaces
JO - Banach Center Publications
PY - 2008
VL - 81
IS - 1
SP - 567
EP - 612
AB - We study the solvability in anisotropic Besov spaces $B_{p,q}^{σ/2,σ}(Ω^T)$, 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 $B_{p,q}^{σ/2 + 1,σ + 2}(Ω^T)$ 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.
LA - eng
KW - boundary slip conditions; Besov regularity of solutions; compressible Navier-Stokes systems; anisotropic Besov spaces
UR - http://eudml.org/doc/281623
ER -