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Solutions of the Navier‐Stokes initial value problem in weighted L q ‐spaces
Author(s) -
Fröhlich Andreas
Publication year - 2004
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.200310170
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , weight function , space (punctuation) , boundary value problem , class (philosophy) , boundary (topology) , mathematical analysis , function (biology) , boundary values , function space , navier–stokes equations , pure mathematics , combinatorics , physics , thermodynamics , philosophy , linguistics , computer science , compressibility , biology , artificial intelligence , evolutionary biology
The problem of strong solvability of the nonstationary Navier‐Stokes equations is considered in weighted L q ‐spaces L q ω (Ω), where the domain Ω ⊂ ℝ n is the half space ℝ n + or a bounded domain with boundary of class C 1,1 and the weight ω belongs to the Muckenhoupt class A q . We give general conditions on the weight function ensuring the existence of a unique strong solution at least locally in time. In particular, these conditions admit weight functions ω ∈ A q , which become singular at the boundary or, in the case Ω = ℝ n + , grow for | x | →∞. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)