TY - JOUR
A2 - Fiorenza, Alberto
AU - Abadias, Luciano
AU - Miana, Pedro J.
PY - 2019
DA - 2019/02/07
TI - Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators
SP - 4763450
VL - 2019
AB - In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf, 0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. Firstly, we give remarkable pointwise and integral inequalities involving the fractional powers (-A)α for 0≤α≤1. We use these estimates to obtain Lp-decayment of solutions of the above quasigeostrophic equation. These results extend the case of fractional derivatives (taking A=Δ, the Laplacian), which has been studied in the literature.
SN - 2314-8896
UR - https://doi.org/10.1155/2019/4763450
DO - 10.1155/2019/4763450
JF - Journal of Function Spaces
PB - Hindawi
KW -
ER -