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DIFFINCL SIGNED

Differential Inclusions and Fluid Mechanics

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EC-Contrib. €

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Project "DIFFINCL" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAET LEIPZIG 

Organization address
address: RITTERSTRASSE 26
city: LEIPZIG
postcode: 4109
website: www.uni-Ieipzig.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 1˙860˙875 €
 EC max contribution 1˙860˙875 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-COG
 Funding Scheme ERC-COG
 Starting year 2017
 Duration (year-month-day) from 2017-04-01   to  2022-03-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAET LEIPZIG DE (LEIPZIG) coordinator 1˙860˙875.00

Map

 Project objective

Important problems in science often involve structures on several distinct length scales. Two typical examples are fine phase mixtures in solid-solid phase transitions and the complex mixing patterns in turbulent or multiphase flows. The microstructures in such situations influence in a crucial way the macroscopic behavior of the system, and understanding the formation, interaction and overall effect of these structures is a great scientific challenge. Although there is a large variety of models and descriptions for such phenomena, a recurring issue in the mathematical analysis is that one has to deal with very complex and highly non-smooth structures in solutions of the associated partial differential equations.

A common ground is provided by the analysis of differential inclusions, a theory whose development was strongly influenced by the influx of ideas from the work of Gromov on partial differential relations, building on celebrated constructions of Nash for isometric immersions, and the work of Tartar in the study of oscillation phenomena in nonlinear partial differential equations. A recent success of this approach is provided by my work on the h-principle in fluid mechanics and Onsager's conjecture. Against this background my aim in this project is to go significantly beyond the state of the art, both in terms of the methods and in terms of applications of differential inclusions. One part of the project is to continue my work on fluid mechanics with the ultimate goal to address important challenges in the field: providing an analytic foundation for the K41 statistical theory of turbulence and for the behavior of turbulent flows near instabilities and boundaries. A further aim is to explore rigidity phenomena and to attack several outstanding open problems in the context of differential inclusions, most prominently Morrey's conjecture on quasiconvexity and rank-one convexity.

 Publications

year authors and title journal last update
List of publications.
2019 Wentao Cao, László Székelyhidi
Very weak solutions to the two-dimensional Monge-Ampére equation
published pages: 1041-1056, ISSN: 1674-7283, DOI: 10.1007/s11425-018-9516-7
Science China Mathematics 62/6 2019-10-07
2019 Wentao Cao, László Székelyhidi
C 1,α isometric extensions
published pages: 613-636, ISSN: 0360-5302, DOI: 10.1080/03605302.2019.1581806
Communications in Partial Differential Equations 44/7 2019-10-07
2018 Stefano Modena, László Székelyhidi
Non-uniqueness for the Transport Equation with Sobolev Vector Fields
published pages: , ISSN: 2199-2576, DOI: 10.1007/s40818-018-0056-x
Annals of PDE 4/2 2019-10-07
2019 Camillo De Lellis, László Székelyhidi
On Turbulence and Geometry: from Nash to Onsager
published pages: 1, ISSN: 0002-9920, DOI: 10.1090/noti1868
Notices of the American Mathematical Society 66/05 2019-10-07
2019 Wentao Cao and László Székelyhidi Jr.
Global Nash-Kuiper theorem for compact manifolds
published pages: , ISSN: , DOI:
2019-10-07
2018 Tristan Buckmaster, Camillo De Lellis, László Székelyhidi, Vlad Vicol
Onsager\'s Conjecture for Admissible Weak Solutions
published pages: 229-274, ISSN: 0010-3640, DOI: 10.1002/cpa.21781
Communications on Pure and Applied Mathematics 72/2 2019-10-07
2019 Wentao Cao, Feimin Huang, Difan Yuan
Global Entropy Solutions to the Gas Flow in General Nozzle
published pages: 3276-3297, ISSN: 0036-1410, DOI: 10.1137/19m1249436
SIAM Journal on Mathematical Analysis 51/4 2019-10-07
2019 Daniel Faraco, Sauli Lindberg and László Székelyhidi Jr.
Bounded solutions of ideal MHD with compact support in space-time
published pages: , ISSN: , DOI:
2019-10-07
2018 Modena, Stefano; Székelyhidi Jr, László
Non-renormalized solutions to the continuity equation
published pages: , ISSN: , DOI:
1 2019-10-07
2019 Modena, Stefano; Sattig, Gabriel
Convex integration solutions to the transport equation with full dimensional concentration
published pages: , ISSN: , DOI:
1 2019-10-07
2018 Clemens Förster, László Székelyhidi
Piecewise Constant Subsolutions for the Muskat Problem
published pages: 1051-1080, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3245-2
Communications in Mathematical Physics 363/3 2019-04-18

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