Conditions for the existence of a global strong solution to a class of nonlinear evolution equations in a Hilbert space

2008

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DOI 10.1134/s0081543808010148
Data confidence 70 medium
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Abstract

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.