Geodesic
Examples of Equations of Navier–Stokes Type Not Strongly Solvable in the Large
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 771-779

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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. 
M. Otelbaev. Examples of Equations of Navier–Stokes Type Not Strongly Solvable in the Large. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 771-779. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a10/
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