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This article is cited in 1 scientific paper (total 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.
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
Linking options:
https://www.mathnet.ru/eng/mzm3897https://doi.org/10.4213/mzm3897 https://www.mathnet.ru/eng/mzm/v89/i5/p771
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Abstract page: | 1474 | Full-text PDF : | 286 | References: | 90 | First page: | 139 |
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