# Compact Course on Mathematical Aspects of Euler Equations

Dates : January 21 - February 01, 2019 Venue : TIFR Center for Applicable Mathematics, Bangalore

## Speaker

Eduard Feireisl

Professor

Institute of Mathematics

Czech Academy of Sciences

Czech Republic

Eduard Feireisl is a Professor of Mathematics in the Institute of Mathematics of the Czech Academy of Sciences. He is a renowned specialist in the mathematical theory of fluid dynamics whose expertise has been recognized by many awards, the latest being the Bernard Bolzano Medal.

## Objectives

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

## Course Contents

- Oscillations, concentrations and how to handle them
- Equations preventing oscillations, compactness and compensated compactness
- Oscillatory solutions to the compressible Euler system
- Oscillatory lemma
- Ill posedness of the Euler system in the space dimension N = 2,3
- Extension of the method to other problems in fluid dynamics

## Schedule

- Januray 22 - January 25, 2019 and January 28 - February 01, 2019
- Lecture 1 : 09:30am to 11:00am
- Tea Break: 11:00am to 11:30am
- Lecture 2 : 11:30am to 01:00pm

## Pre-requisites

The audience should be familiar with Sobolev spaces, functional analysis, and general theory of hyperbolic PDEs.

## Who can apply ?

The course is open to PhD research scholars, post-docs, faculty and scientists working in mathematics departments. Preference will be given to those working on the mathematical aspects of Euler equations.

## How to apply ?

Selection will be made based on your CV and research interests. Please send your latest CV and also ask your advisor to send a recommendation letter to conlaw@tifrbng.res.in

Deadline for application |
21 December, 2018 |

Announcement of selected participants |
24 December, 2018 |

## Support

All selected outstation participants will be paid III AC return train fare from their place of study/work to Bangalore. Boarding and lodging in shared accommodations in the hostel will be provided to outstation participants for the period of the workshop.

## Organizing Committee

- Ujjwal Koley
- Mythily Ramaswamy

## Supported by

- TIFR Centre for Applicable Mathematics, Bangalore
- Airbus Chair on Mathematics of Complex Systems, TIFR-CAM, Bangalore

## List of Selected Participants

## Outstation Participants

- Nibedita Ghosh, Dept. Of Mathematics, IIT Kharagpur
- Tania Biswas, School of Mathematics, IISER Thiruvananthapuram
- P. L. N. Mahendranath, School of Mathematics, IISER Thiruvananthapuram
- Abhrojyoti Sen, School of Mathematical Sciences, NISER Bhubaneswar
- Subha Pal, Dept. Of Mathematical Sciences, Tezpur University
- Prashanta Garain, Dept. Of Mathematics, IIT Kanpur
- Soumyajit Saha, Dept. Of Mathematics, IIT Bombay
- Aekta Aggarwal, Dept. Of Mathematics, IIM Indore
- Sheetal Dharmatti, School of Mathematics, IISER Thiruvananthapuram
- Utpal Manna, School of Mathematics, IISER Thiruvananthapuram
- Soham Sanjay Gokhale, School of Mathematics, IISER Thiruvananthapuram

## Local Participants

- Asha Kisan Dond, IISc
- Gouranga Malik, IISc
- Ramesh Chandra Sau, IISc
- Kunal D. Patil, IISc
- Rahul Biswas, IISc
- Manisha Goyal, ICTS
- Vishal Vasan, ICTS
- K. T. Joseph, TIFR-CAM
- Mythily Ramaswamy, TIFR-CAM
- Ujjwal Koley, TIFR-CAM
- Veerappa Gowda, TIFR-CAM
- Shyam Sundar Ghoshal, TIFR-CAM