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.
Chapter PDF
Similar content being viewed by others
References
Ladyzhenskaya, O.A.: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York (1969)
Temam, R.: Navier-Stokes Equations – Theory and Numerical Analysis. AMS Chelsea Publishing, Providence (2001)
Fursikov, A.V.: On one semilinear parabolic equation of normal type. Mathematics and life sciences. De Gruyter 1, 147–160 (2012)
Fursikov, A.V.: Local Existence Theorems with Unbounded Set of Input Data and Unboundedness of Stable Invariant Manifolds for 3D Navier-Stokes Equations. J. Discr. and Cont. Dyn. Syst. Series S 3(2), 269–290 (2010)
Fujita, H., Kato, T.: On the Navier-Stokes initial value problem. J. Arch. for Rat. Mech. and Anal. 16, 269–315 (1964)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 IFIP International Federation for Information Processing
About this paper
Cite this paper
Fursikov, A. (2013). On the Normal Semilinear Parabolic Equations Corresponding to 3D Navier-Stokes System. In: Hömberg, D., Tröltzsch, F. (eds) System Modeling and Optimization. CSMO 2011. IFIP Advances in Information and Communication Technology, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36062-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-36062-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36061-9
Online ISBN: 978-3-642-36062-6
eBook Packages: Computer ScienceComputer Science (R0)