Thu, 19 Nov 2020
12:00
Virtual

### Explicit bounds for the generation of a lift force exerted by steady-state Navier-Stokes flows over a fixed obstacle

Ph.D. Gianmarco Sperone
(Charles University in Prague)
Abstract

We analyze the steady motion of a viscous incompressible fluid in a two- and three-dimensional channel containing an obstacle through the Navier-Stokes equations under different types of boundary conditions. In the 2D case we take constant non-homogeneous Dirichlet boundary data in a (virtual) square containing the obstacle, and emphasize the connection between the appearance of lift and the unique solvability of Navier-Stokes equations. In the 3D case we consider mixed boundary conditions: the inflow is given by a fairly general datum and the flow is assumed to satisfy a constant traction boundary condition on the outlet. In the absence of external forcing, explicit bounds on the inflow velocity guaranteeing existence and uniqueness of such steady motion are provided after estimating some Sobolev embedding constants and constructing a suitable solenoidal extension of the inlet velocity. In the 3D case, this solenoidal extension is built through the Bogovskii operator and explicit bounds on its Dirichlet norm (in terms of the geometric parameters of the obstacle) are found by solving a variational problem involving the infinity-Laplacian.

The talk accounts for results obtained in collaboration with Filippo Gazzola and Ilaria Fragalà (both at Politecnico di Milano).

Thu, 18 Jun 2020
12:00
Virtual

### A variational approach to fluid-structure interactions

Sebastian Schwarzacher
(Charles University in Prague)
Abstract

I introduce a recently developed variational approach for hyperbolic PDE's. The method allows to show the existence of weak solutions to fluid-structure interactions where a visco-elastic bulk solid is interacting with an incompressible fluid governed by the unsteady Navier Stokes equations. This is a joint work with M. Kampschulte and B. Benesova.

Mon, 25 Feb 2019

16:00 - 17:00
L4

### Diffeomorphic Approximation of W^{1,1} Planar Sobolev Homeomorphisms

Stanislav Hencl
(Charles University in Prague)
Abstract

Let $\Omega\subseteq\mathbb{R}^2$ be a domain and let $f\in W^{1,1}(\Omega,\mathbb{R}^2)$ be a homeomorphism (between $\Omega$ and $f(\Omega)$). Then there exists a sequence of smooth diffeomorphisms $f_k$ converging to $f$ in $W^{1,1}(\Omega,\mathbb{R}^2)$ and uniformly. This is a joint result with A. Pratelli.

Mon, 21 Nov 2016

16:00 - 17:00
L4

### Variational integrals with linear growth

Miroslav Bulíček
(Charles University in Prague)
Abstract
We investigate the properties of certain elliptic systems leading, a priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called Uhlenbeck structure, then the solution can in fact be understood as a standard weak solution, with one proviso: analogously as in the case of minimal surface equations, the attainment of the boundary value is penalized by a measure supported on (a subset of) the boundary, which, for the problems under consideration here, is the part of the boundary where a Neumann boundary condition is imposed. Finally, we will connect such elliptic systems with certain problems in elasticity theory – the limiting strain models.
Subscribe to Charles University in Prague