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Peter Constantin, U. Princeton  OMP 1, Lecture Room 5 (Ground floor)  Fri, 14. Dec 18, 16:00 
Remarks on some mathematical problems in hydrodynamics  

Marco Sammartino, U. Palermo  WPI, OMP 1, Seminar Room 08.135  Sat, 15. Dec 18, 10:00 
2D analytic solutions of Euler equations with concentrated vorticity  

Emil Wiedemann; U. Hannover  WPI, OMP 1, Seminar Room 08.135  Sat, 15. Dec 18, 11:00 
The viscosity limit with boundaries and interfaces: some remarks  
It is a notorious and classical problem whether Leray solutions of the NavierStokes equations converge to a solution of the Euler equations, as viscosity tends to zero. The problem is only wellunderstood in the case that the Euler solution is smooth and there are no physical boundaries. If one (or both) of these requirements are violated, the problem is still largely open. We discuss two specific situations: First, we prove a version of Onsager's conjecture in bounded domains that gives rise to a statement on the viscosity limit and the absence of anomalous dissipation (joint work with C. Bardos and E. S. Titi). Secondly, we discuss the viscosity limit problem for the (nonsmooth) shear flow, also departing from work with Bardos and Titi; we investigate in particular the question what happens when the initial data is not exactly fixed along the viscosity sequence (in progress).  

Vlad Vicol, U. Princeton  WPI, OMP 1, Seminar Room 08.135  Sat, 15. Dec 18, 16:00 
Convex integration on thin sets  
I will discuss the construction of wild weak solutions to the NavierStokes equation which are smooth on the complement of a thin set of times (with Haursdorff dimension strictly less than 1). This is based on joint work with T. Buckmaster and M. Colombo.  

Francois Golse, X Paris  WPI, OMP 1, Seminar Room 08.135  Sun, 16. Dec 18, 10:00 
Derivation of Models for the Dynamics of Sprays/Aerosols  
This talk proposes a derivation of the VlasovNavierStokes system used in the modeling of "thin" aerosol flows from a system of Boltzmann equations for a binary gas mixture involving the propellant gas and the dispersed phase in the aerosol. This derivation is formal, in the sense of the program for deriving fluid dynamic limits of the Boltzmann equation laid out in [C. Bardos  F. Golse  C.D. Levermore: J. Stat. Phys. 63 (1991), 323344].  

Agnieska SwierczewkaGwiazda, U. Warsaw  WPI, OMP 1, Seminar Room 08.135  Sun, 16. Dec 18, 11:00 
Measurevalued  strong uniqueness for general conservation laws  
In the last years measurevalued solutions started to be considered as a relevant notion of solutions if they satisfy the socalled measurevalued  strong uniqueness principle. This means that they coincide with a strong solution emanating from the same initial data if this strong solution exists. Following result of Yann Brenier, Camillo De Lellis and Laszlo Szekelyhidi Jr. for incompresible Euler equation, this property has been examined for many systems of mathematical physics, including incompressible and compressible Euler system, compressible NavierStokes system, polyconvex elastodynamics et al. In my talk I will concentrate on results concerning general conservation laws. Our goal is to provide a unified framework for general systems, that would cover the most interesting cases of systems. Following earlier common result with Eduard Feireisl, Piotr Gwiazda and Emil Wiedemann for compresible NavierStokes system, we develop the concept of dissipative measurevalued solution to general hyperbolic systems. The talk is based on joint results with Piotr Gwiazda and Ondrej Kreml.  

Piotr Gwiazda, Polish Academy of Science  WPI, OMP 1, Seminar Room 08.135  Sun, 16. Dec 18, 14:30 
On the Extension of Onsager's Conjecture for General Conservation Laws  
The aim of this talk is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, larger than 1/3, concerning the regularity of the solutions  space of HÃ¶lder continuous functions with the above exponent, that guarantees the conservation of the generalized entropy; regardless of the structure of the genuine nonlinearity in the underlying system.  

Peter Constantin, U. Princeton  WPI Seminarr Room  Sun, 16. Dec 18, 16:00 
TBA  

Edriss S. Titi, U. Texas  WPI, OMP 1, Seminar Room 08.135  Mon, 17. Dec 18, 10:00 
TBA  
TBA  

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