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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we give an overview of the results established in [3] whichprovides the first rigorous derivation of hydrodynamic equations from theBoltzmann equation for inelastic hard spheres in 3D. In particular, we obtain anew system of hydrodynamic equations describing granular flows and proveexistence of classical solutions to the aforementioned system. One of the mainissue is to identify the correct relation between the restitution coefficient(which quantifies the rate of energy loss at the microscopic level) and theKnudsen number which allows us to obtain non trivial hydrodynamic behavior. Insuch a regime, we construct strong solutions to the inelastic Boltzmannequation, near thermal equilibrium whose role is played by the so-calledhomogeneous cooling state. We prove then the uniform exponential stability withrespect to the Knudsen number of such solutions, using a spectral analysis ofthe linearized problem combined with technical a priori nonlinear estimates.Finally, we prove that such solutions converge, in a specific weak sense,towards some hydrodynamic limit that depends on time and space variables onlythrough macroscopic quantities that satisfy a suitable modification of theincompressible Navier-Stokes-Fourier system.

From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system