Global convergence in the strong norm of an iterative method for the nonstationary Navier-Stokes problem

Autor:	M. E. Bogovskii
Rok vydání:	2013
Předmět:	Strong solutions Nonlinear system Iterative method General Mathematics Mathematical analysis Navier stokes Norm (social) Geometric progression Mathematics
Zdroj:	Doklady Mathematics. 87:148-152
ISSN:	1531-8362 1064-5624
DOI:	10.1134/s1064562413020075
Popis:	It is established below that the existence of a strong solution to the nonlinear Navier–Stokes problem with any initial approximation from the class of strong solu� tions is equivalent to the global convergence of the modified iteration sequence to the sought solution in the norm of the class of strong solutions at a conver� gence rate higher than a geometric progression rate with a ratio arbitrarily close to zero. Interestingly, the sought strong solution is not involved in the construc� tion of the modified iteration sequence and, in fact, the global boundedness of this sequence in the norm of the class of strong solutions becomes a criterion for the global solvability of the nonlinear Navier–Stokes problem in the class of strong solutions (for more detail, see Section 2 below).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a411d3277f0d57df49a5be9b1814ef87 https://doi.org/10.1134/s1064562413020075 Zobrazit plný text záznamu Plný text ve formátu PDF