Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces

@article{Wu2006LowerBF,
  title={Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces},
  author={J. Wu},
  journal={Communications in Mathematical Physics},
  year={2006},
  volume={263},
  pages={803-831}
}
  • J. Wu
  • Published 2006
  • Mathematics
  • Communications in Mathematical Physics
  • When estimating solutions of dissipative partial differential equations in Lp-related spaces, we often need lower bounds for an integral involving the dissipative term. If the dissipative term is given by the usual Laplacian −Δ, lower bounds can be derived through integration by parts and embedding inequalities. However, when the Laplacian is replaced by the fractional Laplacian (−Δ)α, the approach of integration by parts no longer applies. In this paper, we obtain lower bounds for the integral… CONTINUE READING
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    References

    SHOWING 1-10 OF 23 REFERENCES
    On the critical dissipative quasi-geostrophic equation
    • 216
    • PDF
    Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces
    • J. Wu
    • Mathematics, Computer Science
    • SIAM J. Math. Anal.
    • 2005
    • 93
    • PDF
    A pointwise estimate for fractionary derivatives with applications to partial differential equations
    • A. Córdoba, D. Córdoba
    • Mathematics, Medicine
    • Proceedings of the National Academy of Sciences of the United States of America
    • 2003
    • 77
    • PDF
    Generalized MHD equations
    • 221
    • PDF
    The complex KdV equation with or without dissipation
    • 15
    • PDF