# Some linear parabolic system in Besov spaces

Ewa Zadrzyńska; Wojciech M. Zajączkowski

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 567-612
- ISSN: 0137-6934

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topEwa 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 -

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