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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 771–779 (Mi mz3897)  

Examples of Equations of Navier–Stokes Type Not Strongly Solvable in the Large

M. Otelbaev

L. N. Gumilev Eurasian National University

Abstract: In the space of functions with values in Hilbert space, we consider the Cauchy problem $u'_t+Au+B(u,u)=f(t)$, $u(0)=0$, $0\le t\le T$. We construct examples of a self-adjoint operator $A\ge E$ and a bilinear transformation $B$ satisfying the condition $\langle B(u,v),v\rangle=0$ such that the Cauchy problem is not strongly solvable.

Keywords: Navier–Stokes equation, self-adjoint operator, bilinear transformation, Cauchy problem, Hilbert space, Sobolev class

DOI: https://doi.org/10.4213/mzm3897

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English version:
Mathematical Notes, 2011, 89:5, 726–733

Bibliographic databases:

UDC: 517.95
Received: 17.07.2007
Revised: 17.05.2008

Citation: M. Otelbaev, “Examples of Equations of Navier–Stokes Type Not Strongly Solvable in the Large”, Mat. Zametki, 89:5 (2011), 771–779; Math. Notes, 89:5 (2011), 726–733

Citation in format AMSBIB
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\by M.~Otelbaev
\paper Examples of Equations of Navier--Stokes Type Not Strongly Solvable in the Large
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\pages 771--779
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\pages 726--733
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