Geodesic
Conditions for the Existence of a Global Strong Solution to a Class of Nonlinear Evolution Equations in a Hilbert Space
Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 202-212 
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. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 202-212. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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