Decay of solutions to dissipative modified quasi-geostrophic equations

Ferreira, Lucas; Niche, César; Planas, Gabriela

doi:10.1090/proc/13280

Decay of solutions to dissipative modified quasi-geostrophic equations
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by Lucas C. F. Ferreira, César J. Niche and Gabriela Planas PDF

Proc. Amer. Math. Soc. 145 (2017), 287-301 Request permission

Abstract:

We are concerned with global weak solutions to dissipative modified quasi-geostrophic equations. By employing the Fourier Splitting method, we show time-polynomial decay of solutions for certain types of $L^p$-initial data. We also prove decay estimates for the difference between the full solution and the solution to the linear part. Our results cover, in particular, the supercritical range of the fractional diffusion.

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