Shallow Water Model for Lakes with Navier slip boundary condition

TL;DR

This paper develops a mathematical model for lake water dynamics incorporating boundary effects and inflow-outflow conditions, proving global existence of solutions with bounded vorticity.

Contribution

It introduces a new shallow water model with Navier slip boundary conditions and proves its global solvability in the $L_{p}$ vorticity class.

Findings

Proved global in time existence of solutions.

Established solvability with $L_{p}$-bounded vorticity.

Model accounts for inflow, outflow, and porous coast effects.

Abstract

We study a model describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom, the porous coast and the inflows and outflows of rivers. We prove the global in time existence result for this model. The solvability is shown in the class of solutions with $L_{p}$-bounded vorticity for any given $p\in (1,\infty]$.