## Differential Equations Seminar: Gianmarco Sperone

#### Charles University (Prague)

**Title:**Steady Navier-Stokes equations in planar domains with obstacle and explicit bounds for unique solvability

**Abstract: **The theory of flight developed by Kutta and Zhukovsky is mainly based on the idea that a cambered surface produces lift through its ability to generate a vortex about itself. Since fluid flows around an obstacle generate vortices which are difficult to locate and to describe, in this talk we analyze the Navier-Stokes equations for the two-dimensional motion of a viscous fluid in the exterior of a fixed obstacle. In a symmetric framework the appearance of forces is strictly related to non-uniqueness of the solution. Explicit bounds on the data ensuring uniqueness are then sought and several functional inequalities (concerning relative capacity, Sobolev embedding, the continuity constant of the Bogovskii operator) are analyzed in detail and new bounds are obtained.

This is joint work with Filippo Gazzola (Politecnico di Milano).