Mihaela Ignatova

Almost Global Existence for the Prandtl Boundary Layer Equations

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within

On well-posedness and small data global existence for an interface damped free boundary fluid–structure model

{\varepsilon}

On the local existence of the free-surface Euler equation with surface tension

ε of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time

On Some Electroconvection Models

{T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}

Critical SQG in Bounded Domains

Tε≧exp(ε-1/log(ε-1)).

The Harnack inequality for second-order elliptic equations with divergence-free drifts

We address a fluid-structure interaction model describing the motion of an elastic body immersed in an incompressible fluid. We establish a priori estimates for the local existence of solutions for a class of initial data which also guarantees uniqueness.