Some linear parabolic system in Besov spaces

• Autorzy: Ewa Zadrzyńska , Wojciech M. Zajączkowski
• Języki publikacji: 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.

Kategorie tematyczne

• 35K40: Second-order parabolic systems
• 35K45: Initial value problems for second-order parabolic systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 567-612

Daty

wydano

2008

Twórcy

autor

Ewa Zadrzyńska

• Faculty of Mathematics and Information Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland

autor

Wojciech M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc81-0-36