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A solution to parabolic system with the fractional Laplacian

A solution to parabolic system with the fractional Laplacian The existence of a solution to the parabolic system with the fractional Laplacian (−Δ) α/2, α > 0 is proven, this solution decays at different rates along different time sequences going to infinity. As an application, the existence of a solution to the generalized Navier-Stokes equations is proven, which decays at different rates along different time sequences going to infinity. The generalized Navier-Stokes equations are the equations resulting from replacing −Δ in the Navier-Stokes equations by (−Δ) m , m > 0. At last, a similar result for 3-D incompressible anisotropic Navier-Stokes system is obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

A solution to parabolic system with the fractional Laplacian

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH
Subject
Mathematics; Applications of Mathematics; Mathematics, general
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-009-2084-5
Publisher site
See Article on Publisher Site

Abstract

The existence of a solution to the parabolic system with the fractional Laplacian (−Δ) α/2, α > 0 is proven, this solution decays at different rates along different time sequences going to infinity. As an application, the existence of a solution to the generalized Navier-Stokes equations is proven, which decays at different rates along different time sequences going to infinity. The generalized Navier-Stokes equations are the equations resulting from replacing −Δ in the Navier-Stokes equations by (−Δ) m , m > 0. At last, a similar result for 3-D incompressible anisotropic Navier-Stokes system is obtained.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Jun 10, 2009

References

  • Integration by parts formula for regional fractional Laplacian
    Guan, Q. Y.
  • Beyond Brownian motion
    Klafter, J.; Shlesiger, M. F.; Zumofen, G.
  • The random walk’s guide to anomalous diffusion: a fractional dynamics approach
    Metzler, R.; Klafter, J.
  • Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow
    Solomon, T. H.; Weeks, E. R.; Swinney, H. L.
  • Stochastic problems in Physics and Astronomy
    Chandrasekhar, S.
  • Elliptic and parabolic problems
    Cazenave, T.; Dickstein, F.; Weissler, F. B.
  • Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
    Wu, J. H.
  • Chaotic behavior of solutions of the Navier-Stokes system in R N
    Cazenave, T.; Dickstein, F.; Weissler, F. B.
  • Mathematical Geophysics, An introduction to rotating fluids and the Navier-Stokes equations
    Chemin, J. Y.; Desjardins, B.; Gallagher, I.
  • Geophysical Fluid Dynamics
    Pedlovsky, J.
  • On the influence of the earth’s rotation on ocean currents
    Ekman, V. W.
  • Ekman layers of rotating fluids, the case of well prepared initial data
    Grenier, E.; Masmoudi, N.
  • Fluids with anisotropic viscosity
    Chemin, J. Y.; Desjardins, B.; Gallagher, I.
  • A uniqueness result for the Navier-Stokes equations with vanishing vertical viscosity
    Iftimie, D.
  • Well-posedness of the Cauchy problem for the fractional power dissipative equations
    Miao, C. X.; Yuan, B. Q.; Zhang, B.
  • Asymptotic behavior, as t→∞, of solutions of Navier-Stokes equations and nonlinear spectral manifolds
    Foias, C.; Saut, J. C.