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The 3 D incompressible Navier–Stokes equations with partial hyperdissipation
Author(s) -
Yang Wanrong,
Jiu Quansen,
Wu Jiahong
Publication year - 2019
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.201700176
Subject(s) - mathematics , compressibility , dissipation , logarithm , uniqueness , navier–stokes equations , mathematical analysis , reduction (mathematics) , type (biology) , geometry , physics , mechanics , thermodynamics , ecology , biology
The three‐dimensional incompressible Navier–Stokes equations with the hyperdissipation( − Δ ) γ always possess global smooth solutions when γ ≥ 5 4 . Tao [6] and Barbato, Morandin and Romito [1] made logarithmic reductions in the dissipation and still obtained the global regularity. This paper makes a different type of reduction in the dissipation and proves the global existence and uniqueness in the H 1 ‐functional setting.
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