arXiv subjects
Publications and source records attributed to Matthew D. Novack.
The purpose of this note is to study the weak solutions to the inviscid quasi-geostrophic system for initial data belonging to Lebesgue spaces. We give a global existence result as well as detail the connections between several different notions of weak solutions. In addition, we give a condition under which the energy of the system is conserved.
In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly large). This system couples an inviscid transport equation in $\mathbb{R}^3_+$ with an equation on the boundary satisfied by the trace. The proof combines the De Giorgi regularization effect on the boundary $z=0$ -similar to the so called surface quasi-geostrophic equation- with Beale-Kato-Majda techniques to propagate regularity for $z>0$. A potential theory argument is used to strengthen the regularization effect on the trace up to the Besov space $\mathring{B}_{\infty,\infty}^1$.