On the Normal Semilinear Parabolic Equations Corresponding to 3D Navier-Stokes System

Abstract : The semilinear normal parabolic equations corresponding to 3D Navier-Stokes system have been derived. The explicit formula for solution of normal parabolic equations with periodic boundary conditions has been obtained. It was shown that phase space of corresponding dynamical system consists of the set of stability (where solutions tends to zero as time t → ∞), the set of explosions (where solutions blow up during finite time) and intermediate set. Exact description of these sets has been given.
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Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.338-347, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_34〉
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Andrei Fursikov. On the Normal Semilinear Parabolic Equations Corresponding to 3D Navier-Stokes System. Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.338-347, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_34〉. 〈hal-01347554〉

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