Steady solutions to viscous shallow water equations. The case of heavy water.

摘要

In this note, we show the existence of regular solutions to the stationaryversion of the Navier-Stokes system for compressible fluids with a densitydependent viscosity, known as the shallow water equations. For arbitrary largeforcing we are able to construct a solution, provided the total mass issufficiently large. The main mathematical part is located in the constructionof solutions. Uniqueness is impossible to obtain, since the gradient of thevelocity is of magnitude of the force. The investigation is connected to thecorresponding singular limit as Mach number goes to zero and methods for weaksolutions to the compressible Navier-Stokes system.