This article is cited in 1 paper

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.

UDC: 517.95

Received: 17.07.2007
Revised: 17.05.2008

DOI: 10.4213/mzm3897

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

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