arXiv subjects

Pierre Gonin--Joubert

Publications and source records attributed to Pierre Gonin--Joubert.

4 recordsLinked to original sources

arXiv2026

Pressure and temperature relaxation limit for a one-velocity Baer-Nunziato model

The dynamics of two-phase flows out of mechanical and thermal equilibrium are described by a partially dissipative first-order quasilinear system with stiff interaction terms associated with fast relaxation scales. In this paper, we analyze from a mathematical point of view the resulting pressure and temperature relaxation singular limit problem for a one velocity Baer-Nunziato model. This leads to a singular limit problem involving two small parameters. We propose a uniform symmetrization of this system which allows us to justify the strong relaxation limit and to establish a convergence rate for classical solutions.

math.AP↗

arXiv2026

Vanishing conductivity limit for the 1D compressible Navier-Stokes system

The present article studies solutions to the compressible Navier-Stokes equations for ideal gases in one dimension when thermal conductivity is present but very weak, while viscosity is positive and constant. The main novelty is the establishment of bounds that do not explode when the conductivity coefficient approaches zero. The conductivity coefficient is assumed to be constant and the framework is that of ''{à} la Hoff'' solutions. More precisely, the velocity is initially assumed to be regular, while the density and temperature are only in L^infini and far from zero. A new proof of a stability result for cases without conductivity is given. Then, the proof of the zero-conductivity limit to the Navier-Stokes system without conduction is established in the ''{à} la Hoff'' framework.

math.AP↗

arXiv2026

Global in time justification of a two-phase averaged system for heat-conducting ideal gases

In this article, we mathematically justify (globally in time) a Baer-Nunziato type system from the non-isentropic compressible Navier-Sokes equations for heat conducting ideal gases posed over the torus and in one space dimension. The breakthrough in this paper is to define and prove the global existence of solutions in a framework intermediate between weak and strong solutions and then to derive the system through homogenization and Young measures characterization. Note that the main difficulty is to derive a priori uniform bounds on appropriate unknowns in the presence of piecewise constant coefficients (viscosity and adiabatic constants) exhibiting rapid oscillations between two positive values.

math.AP↗

arXiv2026

On the relaxation towards mechanical equilibrium for two-pressure compressible flows

We introduce a symmetrization of a one-velocity two-pressures Baer-Nunziato type model for mixtures of barotropic compressible fluids. It allows us to justify the zero compaction viscosity limit and to recover a solution of the so-called Kapila model. On the other hand, the symmetrization highlights a pressure-induced stabilization mechanism which allows us to recover a global-in-time existence result for initial data close to constant states.

math.AP↗