30 citations · 34 across the 20 of their papers we have counts for
23 papers
Long-time dynamics of partially dissipative hyperbolic systems with non-autonomous coefficients
Timothée Crin-Barat, Ling-Yun Shou, Qimeng Zhu
We study quasilinear symmetrizable partially dissipative hyperbolic systems with non-autonomous relaxation coefficients in (). The existence of global strong…
On the decay estimates of a nonlocal convection-diffusion Hamer system
Timothée Crin-Barat, Belkacem Said-Houari
We consider the multi-dimensional Hamer model for radiating gases in its coupled hyperbolic--elliptic formulation. By means of energy estimates, we establish the global well-posedn…
Pressure and temperature relaxation limit for a one-velocity Baer-Nunziato model
Cosmin Burtea, Timothée Crin-Barat, Pierre Gonin--Joubert
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 assoc…
The compressible Euler system with damping in hybrid Besov spaces: global well-posedness and relaxation limit
Timothée Crin-Barat, Zihao Song
We investigate the global well-posedness of the compressible Euler system with damping in Rd (d\geq1) and its relaxation limit toward the porous medium equation. In [12], the first…
On the relaxation towards mechanical equilibrium for two-pressure compressible flows
Cosmin Burtea, Timothée Crin-Barat, Pierre Gonin--Joubert
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 v…
Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit
Timothée Crin-Barat, Xinghong Pan, Ling-Yun Shou +1
We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form in $\m…
Global convergence rates in the relaxation limits for the compressible Euler and Euler-Maxwell systems in Sobolev spaces
Timothée Crin-Barat, Yue-Jun Peng, Ling-Yun Shou
We study two relaxation problems in the class of partially dissipative hyperbolic systems: the compressible Euler system and the compressible Euler-Maxwell system. In classical Sob…
Large-Time Asymptotics for Hyperbolic Systems with Non-Symmetric Relaxation: An Algorithmic Approach
Timothée Crin-Barat, Lorenzo Liverani, Ling-Yun Shou +1
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abs…
Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness
Timothée Crin-Barat, Nicola De Nitti, Stefan Škondrić +1
We characterize the Leray--Hopf solutions of the 2D inhomogeneous Navier--Stokes system that become strong for positive times. This characterization relies on the strong energy ine…
A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system
Timothée Crin-Barat, Yue-Jun Peng, Ling-Yun Shou +1
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semi…
Relative Energy Method For Weak-Strong Uniqueness Of The Inhomogeneous Navier-Stokes Equations
Timothée Crin-Barat, Stefan Škondrić, Alessandro Violini
We present a weak-strong uniqueness result for the inhomogeneous Navier-Stokes (INS) equations in () for bounded initial densities that are far from vacuum. G…
Asymptotic-preserving finite difference method for partially dissipative hyperbolic systems
Timothée Crin-Barat, Dragoş Manea
In this paper, we analyze the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a discrete setting. We prove that one of the simpl…
The Cattaneo-Christov approximation of Fourier heat-conductive compressible fluids
Timothée Crin-Barat, Shuichi Kawashima, Jiang Xu
We investigate the Navier-Stokes-Cattaneo-Christov (NSC) system in (), a model of heat-conductive compressible flows serving as a finite speed of propagation…
Strong relaxation limit and uniform time asymptotics of the Jin-Xin model in the framework
Timothée Crin-Barat, Ling-Yun Shou, Jianzhong Zhang
We investigate the time-asymptotic stability of the Jin-Xin model and its diffusive relaxation limit toward viscous conservation laws in for . First, we est…
Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: application to the nonlinearly damped p-system
Timothée Crin-Barat, Ling-Yun Shou, Enrique Zuazua
A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability…
Diffusive relaxation limit of the multi-dimensional hyperbolic Jin-Xin system
Timothée Crin-Barat, Ling-Yun Shou
We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a con…
Quantitative derivation of a two-phase porous media system from the one-velocity Baer-Nunziato and Kapila systems
Timothée Crin-Barat, Ling-Yun Shou, Jin Tan
In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-fluid models…
Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation
Roberta Bianchini, Timothée Crin-Barat, Marius Paicu
We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in $\dot H^{1-τ}(\mathbb{R}^2…
On the decay of one-dimensional locally and partially dissipated hyperbolic systems
Timothée Crin-Barat, Nicola De Nitti, Enrique Zuazua
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the cl…
Global existence for partially dissipative hyperbolic systems in the Lp framework, and relaxation limit
Timothée Crin-Barat, Raphaël Danchin
Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to ex…
The hyperbolic-parabolic chemotaxis system for vasculogenesis: global dynamics and relaxation limit toward a Keller-Segel model
Timothée Crin-Barat, Qingyou He, Ling-Yun Shou
An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For small initial…
Partially dissipative hyperbolic systems in the critical regularity setting : The multi-dimensional case
Timothée Crin-Barat, Raphaël Danchin
We are concerned with quasilinear symmetrizable partially dissipative hyperbolic systems in the whole space with . Following our recent work [10] dedicated t…
Partially dissipative one-dimensional hyperbolic systems in the critical regularity setting, and applications
Timothée Crin-Barat, Raphael Danchin
Here we develop a method for investigating global strong solutions of partially dissipative hyperbolic systems in the critical regularity setting. Compared to the recent works by K…