• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

It is a notorious and classical problem whether Leray solutions of the Navier-Stokes equations converge to a solution of the Euler equations, as viscosity tends to zero. The problem is only well-understood 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 (non-smooth) 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).

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

I will discuss the construction of wild weak solutions to the Navier-Stokes 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.

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

This talk proposes a derivation of the Vlasov-Navier-Stokes 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), 323-344].

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued - 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 Navier-Stokes 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 Navier-Stokes system, we develop the concept of dissipative measure-valued solution to general hyperbolic systems. The talk is based on joint results with Piotr Gwiazda and Ondrej Kreml.

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

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 Hölder 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.

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

• Thematic program: Models in Plasmas, Earth and Space Science (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)

TBA

• Thematic program: Mathematics for Materials and Micromagnetism (2018/2019)
• Event: Workshop on "Mathematical Amelioration in Fluid Dynamics" (2018)