Mathematics Colloquim: Weak-strong uniqueness principle for dissipative measure-valued solutions
Prof. Piotr Gwiazda
University of Warsaw, Poland
Speaker |
Prof. Piotr Gwiazda
University of Warsaw, Poland
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When |
Nov 02, 2022
from 04:00 PM to 05:00 PM |
Where | Auditorium, Ground Floor and via zoom |
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Abstract: We will start with the statement of weak-strong uniqueness principle for general hyperbolic conservation laws and show that Euler-Poisson system fails to fit into this framework. We consider several pressureless variants of the compressible Euler
equation driven by nonlocal repulsion-attraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued solutions, i.e., very weak solutions described by a classical Young measure together with appropriate concentration defects. We then investigate the evolution of a relative energy functional to compare a measure-valued solution to a regular solution emanating from the same initial datum. This leads to a (partial) weak-strong uniqueness principle.
equation driven by nonlocal repulsion-attraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued solutions, i.e., very weak solutions described by a classical Young measure together with appropriate concentration defects. We then investigate the evolution of a relative energy functional to compare a measure-valued solution to a regular solution emanating from the same initial datum. This leads to a (partial) weak-strong uniqueness principle.