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Course, academic year 2019/2020
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New results in the theory of Euler equations - NMMA623
Title in English: Nové výsledky v teorii Eulerových rovnic
Guaranteed by: Matematický ústav AV ČR, v.v.i. (32-MUAV)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Note: you can enroll for the course repeatedly
Guarantor: Mgr. Ondřej Kreml, Ph.D.
Class: DS, matematická analýza
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Interchangeability : NDIR248
Annotation -
Last update: G_M (08.05.2014)
In this lecture we will present elegant method recently developed by C. De Lellis and L. Székelyhidi which yields surprising results concerning weak solutions of incompressible and compressible Euler equations. In particular we will prove existence of infinitely many global bounded weak solutions of incompressible Euler equations with compact support in space-time. We will also show applications of this method on compressible Euler equations and on searching for initial data yielding infinitely many weak solutions. For master and doctoral students.
Literature -
Last update: G_M (08.05.2014)

[1] DE LELLIS, C., SZÉKELYHIDI, L.J.: The Euler equations as a

differential inclusion. Ann. Math. 170, no. 3, 1417-1436 (2009)

[2] DE LELLIS, C., SZÉKELYHIDI, L.J.: On admissibility criteria for weak

solutions of the Euler equations. Arch. Ration. Mech. Anal. 195, no. 1,

225-260 (2010)

[3] DE LELLIS, C., SZÉKELYHIDI, L.J.: The h-principle and the equations of

fluid dynamics. Bull. Amer. Math. Soc. (N.S.) 49, no. 3, 347-375 (2012)

Syllabus -
Last update: G_M (08.05.2014)

In this lecture we will present elegant method recently

developed by C. De Lellis and L. Székelyhidi which yields surprising

results concerning weak solutions of incompressible and compressible Euler

equations. In particular we will prove existence of infinitely many global

bounded weak solutions of incompressible Euler equations with compact

support in space-time. We will also show applications of this method on

compressible Euler equations and on searching for initial data yielding

infinitely many weak solutions.

For master and doctoral students.

 
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