Analysis and Applied Mathematics Seminar
Daniel Lear Claveras
UIC
Stability Near Hydrostatic Equilibrium in Fluid Mechanics
Abstract: A fluid is said to be in hydrostatic equilibrium when it is at rest. Then the forces acting on it must balance it. A natural question therefore arises:
What happens if our initial data is close to an hydrostatic equilibrium solution?
The field of hydrodynamic stability has a long history starting in the 19th century. For us, the basic problem is to consider a perturbation of the hydrostatic equilibrium, in which case the fluid must start to move, and to study the long-time behavior of the solution. In this talk, we study the stability of the hydrostatic equilibrium in two different problems.
1st: The inviscid incompressible porous media equation.
2nd: The inviscid and non-diffusive Boussinesq system with a velocity damping term.
Monday September 30, 2019 at 4:00 PM in 636 SEO