×

Some linear parabolic system in Besov spaces. (English) Zbl 1173.35067

Rencławowicz, Joanna (ed.) et al., Parabolic and Navier-Stokes equations. Part 2. Proceedings of the confererence, Bȩdlewo, Poland, September 10–17, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 81, Pt. 2, 567-612 (2008).
The authors are interested in an initial-boundary value problem for a linear parabolic system
\[ u_t -\text{ div} {\mathbb D}(u) = f \quad \text{in}\quad (0,T)\times \Omega \]
\(\Omega\) is a bounded domain in \({\mathbb R}^3\) and \(T<\infty\). The system arises in the study of the compressible Navier-Stokes systems with boundary slip conditions. The solvability of the parabolic system is examined in anisotropic Besov spaces with positive smoothness parameter. Under some technical assumptions the existence of unique solution is proved.
For the entire collection see [Zbl 1147.35006].

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
PDFBibTeX XMLCite
Full Text: Link