Sesión Ecuaciones Diferenciales y aplicacionesPatterns and equilibria in incompressible fluids
Claudia García
Universidad de Granada, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
The motion of a uniform incompressible fluid is described by the Navier-Stokes equations and, in its inviscid regime, via the Euler equations. In the two-dimensional case, the Euler equations in the vorticity formulation contain many interesting relative equilibria: stationary, rotating and translation solutions. Bifurcation theory arises naturally in the study of many PDE’s, which can be characterized by an implicit equation of the form
\begin{equation} F(\lambda,x)=0, \end{equation}
where $\lambda\in\mathbb{R}$ and $x$ belongs to some infinite-dimensional Banach space. In this talk, we will take advantage of this theory to review the existence of different kind of solutions: V-states, non uniform rotating vortices or Karman Vortex Street type of solutions, among others. All those simplified dynamics are governed by a nonlinear and nonlocal equation of type (1).