ICTS:29950

Video URL

A short but up-to-date introduction to partially parabolic or dissipative hyperbolic systems - IV

A short but up-to-date introduction to partially parabolic or dissipative hyperbolic systems - IV

(2024). A short but up-to-date introduction to partially parabolic or dissipative hyperbolic systems - IV. SciVideos. https://youtu.be/cpUegIfpJaw

A short but up-to-date introduction to partially parabolic or dissipative hyperbolic systems - IV. SciVideos, Oct. 04, 2024, https://youtu.be/cpUegIfpJaw 

          @misc{ scivideos_ICTS:29950,
            doi = {},
            url = {https://youtu.be/cpUegIfpJaw},
            author = {},
            keywords = {},
            language = {en},
            title = {A short but up-to-date introduction to partially parabolic or dissipative hyperbolic systems - IV},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:29950 see, \url{https://scivideos.org/icts-tifr/29950}}
          }
Raphaël Danchin
Talk numberICTS:29950
Source RepositoryICTS-TIFR
Source EventDeterministic and Stochastic Analysis of Euler and Navier-Stokes Equations
Collection

Abstract

Many physical phenomena may be modeled by first order symmetric hyperbolic equations with degenerate dissipative or diffusive terms. This is the case in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term.
Such so-called partially dissipative or diffusive systems have been extensively studied by S .Kawashima in his PhD thesis from 1984. For a rather general class of systems he pointed out a simple necessary condition for the global existence of solutions in the vicinity of constant solutions.
This condition that is nowadays named (SK) condition has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. Very recently, advances have been made by T. Crin-B...