English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We prove the uniqueness and stability of entropy shocks to the isentropicEuler systems among all vanishing viscosity limits of solutions to associatedNavier-Stokes systems. To take into account the vanishing viscosity limit, weshow a contraction property for any large perturbations of viscous shocks tothe Navier-Stokes system. The contraction estimate does not depend on thestrength of the viscosity. This provides a good control on the inviscid limitprocess. We prove that, for any initial value, there exists a vanishingviscosity limit to solutions of the Navier-Stokes system. The convergence holdsin a weak topology. However, this limit satisfies some stability estimatesmeasured by the relative entropy with respect to an entropy shock. Inparticular, our result provides the uniqueness of entropy shocks to the shallowwater equation in a class of inviscid limits of solutions to the viscousshallow water equations.

Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems