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A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference…
In this paper, we study both convergence and bounded variation properties of a new fully discrete conservative Lagrangian--Eulerian scheme to the entropy solution in the sense of Kruzhkov (scalar case) by using a weak asymptotic analysis.…
A continuum crowd flow model is reformulated in the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one-dimensional) road traffic flow. Our extension…
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point…
We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukhin in the non-relativistic setting. We establish the…
We establish unique existence and stability of subsonic potential flow for steady Euler-Poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on non-insulated boundary from a fixed…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of…
We prove the existence of global weak entropy solutions for a class of non-symmetric Keyfitz-Kranzer type systems that includes lubrication models for thin-film flow. We identify a family of entropy/entropy-flux pairs for these first-order…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. We constrain the flow both analytically…
We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the…
Systems of the first order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of solutions involve in many cases product of distributions. In this paper we study such a…
We consider a model of steady, incompressible non-Newtonian flow with neglected convective term under external forcing. Our structural assumptions allow for certain non-degenerate power-law or Carreau-type fluids. We provide the full-range…
We study a toy model for the evolution of the oxygen concentration in an oxide layer. It consists in a transient convection diffusion equation in a one-dimensional domain of variable width. The motions of the boundaries are governed by the…
Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our…