Existence of global strong solution for the Navier-Stokes Korteweg system in one dimension with degenerate viscosity coefficients
Prof. Boris Haspot, Université Paris-Dauphine, Paris, France
| Speaker |
Prof. Boris Haspot, Université Paris-Dauphine, Paris, France
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|---|---|
| When |
Aug 02, 2022
from 04:00 PM to 05:00 PM |
| Where | Auditorium, Ground Floor |
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Abstract: In the first main result of this talk we prove that one can approximate discontinuous solutions of the $1d$ Navier Stokes system with solutions of the
$1d$ Navier-Stokes-Korteweg system as the capillarity parameter tends to $0$. Moreover, we allow the viscosity coefficients $\mu=\mu\left( \rho\right) $ to degenerate near vacuum.
The second main result states the existence of unique finite-energy global strong solutions for the $1d$ Navier-Stokes system assuming only that $\rho_{0},1/\rho_{0}\in L^{\infty}$. This last result finds itself a natural application in the context of the mathematical modeling of multiphase flows.