Local-in-time existence of strong solutions to an averaged thick sprays model

Victor Fournet; Christophe Buet; Bruno Després

doi:10.3934/krm.2023034

Article Contents

2024, Volume 17, Issue 4: 606-633. Doi: 10.3934/krm.2023034

This issue Previous Article Fractional diffusion limit of a linear Boltzmann model with reflective boundaries in a half-space Next Article A Galerkin type method for kinetic Fokker-Planck equations based on Hermite expansions

Local-in-time existence of strong solutions to an averaged thick sprays model

1.
Laboratoire Jacques Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
2.
CEA, DAM, DIF, F-91297, Arpajon, France
3.
Université Paris-Saclay, CEA DAM DIF, Laboratoire en Informatique Haute Performance pour le Calcul et la simulation, F-91297 Arpajon, France

^*Corresponding author: Victor Fournet
^*Corresponding author: Victor Fournet

Received: December 2022

Revised: September 2023

Early access: October 2023

Published: August 2024

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Abstract

We propose a new system for the modelling of thick sprays. We prove that this system verifies conservation properties together with a maximum principle regarding the volume fraction of the gas. Our main result is that the barotropic version of this system is locally in time well-posed in $ H^s $.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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