BCAM Course | Introduction to Compressible fluids: Part 1 (Weak Solutions) and Part II (Strong Solutions)
Data: Al, Urt 13 - Ar, Mar 18 2025
Ordua: 10:30 - 12:30
Lekua: Maryam Mirzakhani Seminar Room at BCAM
Hizlariak: Arnab Roy (BCAM)
Erregistroa: Course Website and Registration Link
This is an introductory course on Compressible Navier-Stokes equations, spanning 20 hours (2 hours per week over 10 weeks).
The first part of the course (5 weeks: 10 hours) focuses on weak solutions for compressible fluids.
We will prove the existence theory of weak solutions (à la P.L. Lions and E. Feireisl) through the following steps: the continuity equation with dissipation, the vanishing viscosity limit, and the artificial pressure limit. The second part of the course (5 weeks: 10 hours) covers strong solutions for compressible fluids. We will establish the existence and uniqueness of strong solutions, considering both local in time for large data and global in time for small data. Additionally, we will introduce the concept of relative energy, which helps establish weak-strong uniqueness.
More information about the program at the Course Website (Link).
Antolatzaileak:
BCAM
Hizlari baieztatuak:
Arbanb Roy (BCAM)
Currently, the speaker is working in the Basque Center of Mathematics (BCAM) as an Ikerbasque Research Fellow and Ramón y Cajal Fellow. His main area of research is the Fluid flows and Fluid-Structure Interaction (FSI) problems, particularly, existence, uniqueness, long time behaviour and control aspects (controllability, stabilizability and optimal control) of FSI problems. These problems come from different domains of application, such as medicine (blood motion in arter- ies), biology (fish swimming, bird flight, micro-organism motion), civil engineering (bridge construction), naval and aerospace engineering etc. Despite all their practical applications, the mathematical understanding of such models is very challenging due to the involvement of strong nonlinearities and the presence of free boundaries.
The speaker completed his Ph.D from Tata Institute of Fundamental Research, Centre For Applicable Mathematics (TIFR-CAM), Bangalore. He had Postdoctoral research experience in several institutes: INRIA Nancy-Grand Est, France (2019-20), Czech Academy of Science, Prague (2020-2021) and Basque Center of Mathematics (BCAM), Spain (2021-2022) respectively. After that, he was awarded the prestigious Humboldt fellowship (supported by the Alexander von Humboldt-Stiftung / Foundation) for 2 years (2022-2024) and during this time he was working at Technische Universität Darmstadt.