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• # Artykuł - szczegóły

## Banach Center Publications

2008 | 81 | 1 | 567-612

## Some linear parabolic system in Besov spaces

EN

### Abstrakty

EN
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.

567-612

wydano
2008

### Twórcy

autor
• Faculty of Mathematics and Information Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland