Premium
About the Regularity of Solutions of the Nonstationary Navier‐Stokes System
Author(s) -
Chelkak S.,
Koshelev A.
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961770105
Subject(s) - pointwise , uniqueness , mathematics , computation , class (philosophy) , navier–stokes equations , mathematical analysis , numerical analysis , algorithm , compressibility , computer science , mechanics , artificial intelligence , physics
The problem of existence of regular (continuous, Holder continuous) solutions of the nonstationary Navier‐Stokes system is an important one in modern mathematical physics. It is closely connected with two main issues: the uniqueness of the solution and the possibility to apply approximate methods in numerical analysis and practical computations. Pointwise estimates of the velocity fields are essential for different numerical applications. We consider here mainly the multidimensional nonstationarity problem for finite (not necessarily small) times. In this paper we show that for small Reynold's numbers the boundedness of the velocity can be obtained and therefore the existence of unique strong solution can be proved for a certain class of external forces.