Journal
MATHEMATISCHE NACHRICHTEN
Volume 294, Issue 12, Pages 2302-2316Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.201900407
Keywords
energy criteria; Navier-Stokes equations; regularity; Holder continuity; weak solutions
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Funding
- National Foundation for Science and Technology Development [101.02-2020.13]
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The text discusses the regularity of weak solutions of the unstationary Navier-Stokes equations in a general domain and their relationship with kinetic energy. The study extends previous results and provides specific mathematical expressions to support the findings.
Let u be a weak solution of the instationary Navier-Stokes equations in a completely general domain omega subset of R3 which additionally satisfies the strong energy inequality. Firstly, we prove that u is regular if the kinetic energy 12 parallel to u(t)parallel to 22 is left-side Holder continuous with Holder exponent 12 and with a sufficiently small Holder seminorm. This result extends the previous ones by several authors [5, 6, 7, 8] in which the domain omega is additionally supposed to be bounded or have the uniform C-2-boundary partial differential omega. Secondly, we show that if u(t)is an element of D(A14) and lim delta -> 0+parallel to A14(u(t-delta)-u(t))parallel to 2
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