In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
On considère l’équation d’Euler incompressible dans le plan. Dans le cas où le tourbillon est positif et à support compact on montre que le support du tourbillon croît au plus comme , améliorant la borne obtenue par C. Marchioro. Dans le cas où le tourbillon change de signe, on donne un exemple de tourbillon initial tel que la croissance du diamètre du support du tourbillon est exactement . Enfin, dans le cas du demi-plan et du tourbillon initial positif et à support compact, on montre que le...
We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a...