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* Markov selection to the stochastic compressible Navier Stokes system.  * Markov selection to the stochastic compressible Navier Stokes system. 
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* Ill posedness of the stochastic compressible Euler system.  * Ill posedness of the stochastic compressible Euler system. 
Compact Course on Mathematical aspects of stochastic Compressible Fluid Flows
Dates : February 17  February 28, 2020 Venue : TIFR Center for Applicable Mathematics, Bangalore
Speaker
Martina Hofmanova
Professor
Faculty of Mathematics
Bielefeld University
Germany
Martina Hofmanova is a young Professor of Mathematics in the Bielefeld University of Germany. She is a renowned specialist in the mathematical theory of stochastic fluid dynamics, in particular stochastic Navier Stokes and Euler equations. She is also an expert on rough path theory for stochastic partial dierential equations.
Objectives
We introduce our model system and main questions of interest. A particular emphasis is put on various notions of solutions. To begin, we briefly discuss the principal concepts from probability theory and stochastic analysis with applications to stochastic PDEs, and make a short excursion in the theory of compressible NavierStokes equations. As the first step in our analysis of the compressible NavierStokes system driven by stochastic forces we establish existence of a dissipative martingale solution. We also show that they satisfy a relative energy inequality and discuss the long time behaviour of dissipative martingale solutions. Next, we prove existence of strong solutions. These solutions are strong in the PDE and probabilistic sense and can only be showed to exist locally in time, that is, up to a positive stopping time.
Course Contents
 Stochastic compressible Navier Stokes system.
 Weak, Strong, Mild, Stationary solutions to compressible Navier Stokes systems.
 Relative energy inequality for compressible fluids with stochastic forcing and their applications.
 Markov selection to the stochastic compressible Navier Stokes system.
 Ill posedness of the stochastic compressible Euler system.
Schedule
 February 17  February 21, 2020 and February 24  February 28, 2020
 Lecture 1 : 09:30am to 11:00am
 Tea Break: 11:00am to 11:30am
 Lecture 2 : 11:30am to 01:00pm
Prerequisites
The audience should be familiar with functional analysis, stochastic analysis, and deterministic theory of compressible fluid flows.
Who can apply ?
The course is open to PhD research scholars, postdocs, faculty and scientists working in mathematics departments. Preference will be given to those working on the mathematical aspects of Fluid flows.
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 
17 January, 2020 
Announcement of selected participants 
20 January, 2020 
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, TIFRCAM, Bangalore
List of Selected Participants
Outstation Participants