Some linear parabolic system in Besov spaces

Tom 81 / 2008

Ewa Zadrzyńska, Wojciech M. Zaj/aczkowski Banach Center Publications 81 (2008), 567-612 MSC: Primary 35K45, 35K50; Secondary 35K40. DOI: 10.4064/bc81-0-36

Streszczenie

We study the solvability in anisotropic Besov spaces $B_{p,q}^{{\sigma\over2},\sigma}(\Omega^T)$, $\sigma\in\mathbb R_+$, $p,q\in(1,\infty)$ 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 $B_{p,q}^{{\sigma\over2}+1,\sigma+2}(\Omega^T)$ is divided into three steps:

$1^\circ$ 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.

$2^\circ$ Applying the regularizer technique the existence is proved in a~bounded domain.

$3^\circ$ The problem with nonvanishing initial data is solved by an appropriate extension of initial data.

Autorzy

  • Ewa ZadrzyńskaFaculty of Mathematics and Information Sciences
    Warsaw University of Technology
    pl. Politechniki 1
    00-661 Warszawa, Poland
    e-mail
  • Wojciech M. Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-950 Warszawa, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek