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= Compact Course on Mathematical Aspects of Euler Equations = = Compact Course on Mathematical aspects of stochastic Compressible Fluid Flows =
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Dates : January 21 - February 01, 2019 Dates : February 17 - February 28, 2020
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{{attachment:feireisl.jpg ||align="right",width="400"}} {{attachment:Martina-Hofmanova.jpeg ||align="right",width="260"}}
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[[http://www.math.cas.cz/homepage/main_page.php?id_membre=37|Eduard Feireisl]] <<BR>> Professor <<BR>> Institute of Mathematics <<BR>> Czech Academy of Sciences <<BR>> Czech Republic [[https://www.math.uni-bielefeld.de/~hofmanova/|Martina Hofmanova]] <<BR>> Professor <<BR>> Faculty of Mathematics <<BR>> Bielefeld University <<BR>> Germany
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Eduard Feireisl is a Professor of Mathematics in the [[http://www.math.cas.cz|Institute of Mathematics]] of the [[http://www.cas.cz|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. Martina Hofmanova is a young Professor of Mathematics in the [[https://www.uni-bielefeld.de/(en)/|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 di erential equations.
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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. 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 Navier-Stokes equations. As the first step in our analysis of the compressible Navier-Stokes 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.

Reference: [[https://www.degruyter.com/view/product/475854|Stochastically forced compressible fluid flows, De Gruyter Seriesin Applied and Numerical Mathematics, De Gruyter, 2018.]]
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 * 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
 * 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.

 
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   * Januray 22 - January 25, 2019 and January 28 - February 01, 2019    * February 17 - February 21, 2020 and February 24 - February 28, 2020
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   * Lecture 1 : 09:30am to 11:00am    * Lecture : 09:30am to 11:00am
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   * Tea Break: 11:00am to 11:30am

   * Lecture 2 : 11:30am to 01:00pm
   
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The audience should be familiar with Sobolev spaces, functional analysis, and general theory of hyperbolic PDEs. The audience should be familiar with functional analysis, stochastic analysis, and deterministic theory of compressible fluid flows.
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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. 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 Fluid flows.
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||Deadline for application ||21 December, 2018 ||
||Announcement of selected participants ||24 December, 2018 ||
||Deadline for application ||10 January, 2020 ||
||Announcement of selected participants ||14 January, 2020 ||
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 * Kush Kinra, IIT Roorkee
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== Outstation Participants ==  * Jisha CR, SRM University
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  == Local Participants ==  * Sudhir Singh, NIT Trichy
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   * Soham Gokhale, IISER Thiruvananthapuram

 * Divya Jaganathan, ICTS-TIFR

 * Divya Goel, IIT Delhi

 * Ananta Kumar Majee, IIT Delhi

 * Neeraj Bhauryal

 * Saibal Khan

 * Abhishek

 * Utsab Sarkar

 * Adimurthi

 * Imran Biswas

 * G D Veerappa Gowda

 * Mythily Ramaswamy

* Ujjwal Koley

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.jpeg

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 di erential 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 Navier-Stokes equations. As the first step in our analysis of the compressible Navier-Stokes 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.

Reference: Stochastically forced compressible fluid flows, De Gruyter Seriesin Applied and Numerical Mathematics, De Gruyter, 2018.

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 : 09:30am to 11:00am

Pre-requisites

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, post-docs, 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

10 January, 2020

Announcement of selected participants

14 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, TIFR-CAM, Bangalore

List of Selected Participants

  • Kush Kinra, IIT Roorkee
  • Jisha CR, SRM University
  • Sudhir Singh, NIT Trichy
  • Soham Gokhale, IISER Thiruvananthapuram
  • Divya Jaganathan, ICTS-TIFR
  • Divya Goel, IIT Delhi
  • Ananta Kumar Majee, IIT Delhi
  • Neeraj Bhauryal
  • Saibal Khan
  • Abhishek
  • Utsab Sarkar
  • Adimurthi
  • Imran Biswas
  • G D Veerappa Gowda
  • Mythily Ramaswamy

* Ujjwal Koley

AirbusChair: Programs/eqn2020 (last edited 2020-02-18 11:08:26 by shrikant)