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}
}

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