Geodesic
Conditions for the Existence of a~Global Strong Solution to a~Class of Nonlinear Evolution Equations in a~Hilbert Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 202-212.

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We study a nonlinear operator differential equation in a Hilbert space. This equation represents an abstract model for the system of Navier–Stokes equations. The main result consists in proving the existence of a strong solution to this equation under the condition that a certain other system of equations (related to the original equation) has only the zero solution. 
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     title = {Conditions for the {Existence} of {a~Global} {Strong} {Solution} to {a~Class} of {Nonlinear} {Evolution} {Equations} in {a~Hilbert} {Space}},
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M. Otelbaev; A. A. Durmagambetov; E. N. Seitkulov. Conditions for the Existence of a~Global Strong Solution to a~Class of Nonlinear Evolution Equations in a~Hilbert Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 202-212. http://geodesic.mathdoc.fr/item/TM_2008_260_a13/

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