Seminario de Ecuaciones Diferenciales: «Hyperbolic effects in incompressible fluid mechanics»

Seminario impartido por Francesco Fanelli (BCAM).

Resumen:In this talk, we are interested in the well-posedness of certain systems of PDEs arising in models of fluid mechanics and which present a hyperbolic structure. After a short overview of previous results available for the incompressible Euler equations, both in its homogeneous and non-homogeneous versions, we focus on the special case of a system which describes the dynamics of an incompressible fluid having variable density and presenting non-dissipative viscosity effects. Examples of such fluids arise both in quantum and classical hydrodynamics.

At the level of the mathematical model, the non-dissipative nature of the viscosity is encoded by an odd term, dubbed precisely odd viscosity tensor. As the odd viscosity term involves higher order space derivatives of the velocity field and of the density, it is responsible for an apparent loss of regularity in the classical a priori estimates. In this talk, we will show how to circumvent such a loss of derivatives by introducing a set of good unknowns, which allow to highlight a hyperbolic structure underlying the system of equations. As a consequence, we will establish a well-posedness result in the framework of Sobolev spaces of high enough regularity.

The talk is based on a joint work with Rafael Granero-Belinchón (Universidad de Cantabria) and Stefano Scrobogna (Università degli Studi di Trieste).

• Fecha: Lunes, 20 de Noviembre de 2023
• Lugar: Aula A20 – Facultad de Ciencias
• Horario: 10:00h
• Organiza: Instituto de Matemáticas (IMAG)
• Más información: imag@ugr.es