Luigi Berselli

Pisa

Šárka Nečasová

Prague

Ana Silvestre

Lisbon

Luigi Berselli

On the Fourier-Galerkin approximation for 2d incompressible fluids: convergence rates valid for large Reynolds number

We study the uniform-in-time L^2 convergence for the Fourier-Galerkin approximation to 2D Navier-Stokes and Euler equations with bounded vorticity. Precisely, we show that both the approximating velocity and the approximating vorticity converge strongly in C(L^2), with an explicit rate of convergence for the velocity. Related results under different assumptions on the vorticity are also proved, with particular emphasis on the identification of characteristic lengths and times.

Šárka Nečasová

On the problem of interaction of fluid with the structure

In the talk, we will focus on the existence result of compressible fluid with structure. We will describe the situation of motion of a rigid body/bodies in the domain filled by the compressible fluids; secondly, the motion of the compressible fluid around a moving rigid body and thirdly the case when the boundary of the domain is elastic. We show the existence results and moreover, the singular limit in the case of the low Mach number limit, inviscid limit.

This lecture is based on collaborative work with the following authors: K. Bhandari, A. Roy, A. Schlomekemper, M. Ramaswamy, F. Oschmann, T. Eiter, Y. Liu, S. Mitra, S. Kracmar and A. Novotny.

Ana Silvestre

On the Navier-Stokes equations in distorted pipes under dynamic and energy-stable outflow boundary conditions

We consider the evolution of a viscous incompressible fluid in three-dimensional distorted pipes, of finite length, modeled through the Navier-Stokes equations with mixed boundary conditions. Specifically, the inflow is given by general prescribed datum, the outflow is subject to a dynamic condition including a directional do-nothing boundary condition; standard no-slip assumptions are imposed on the remaining walls of the domain. We introduce a new functional framework that accommodates the dynamic boundary condition and the incompressibility constraint. Within this framework, we establish the existence of weak solutions. Moreover, under a smallness assumption on the data, we prove the existence and uniqueness of global strong solutions. This is joint work with Alessio Falocchi (Politecnico di Milano) and Gianmarco Sperone (Pontificia Universidad Católica de Chile).