Global solvability of the Cauchy problem for the Navier–Stokes equation in $$\mathbb {R}^3$$ for some class of initial data

Autor:	W. M. Zaja̧czkowski, K. Pileckas
Rok vydání:	2007
Předmět:	Sobolev space Pure mathematics General Mathematics Norm (mathematics) Mathematical analysis Mathematics::Analysis of PDEs Initial value problem Navier stokes Ball (mathematics) Navier–Stokes equations Mathematics
Zdroj:	Mathematische Zeitschrift. 260:305-327
ISSN:	1432-1823 0025-5874
DOI:	10.1007/s00209-007-0275-4
Popis:	In this paper we prove the existence of regular solutions to the Navier–Stokes equations if the initial data v0 have some finite weighted norm and supp v0 belongs to \(\mathbb {R}^3{\setminus}B_{R_0}\) , \(B_{R_0}\) is a ball with radius R0, where R0 is sufficiently large. The proof follows from appropriate estimates in weighted Sobolev spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e1554ff48909f119433094db9276972c https://doi.org/10.1007/s00209-007-0275-4 Full text from SpringerLink