Related papers: A regularization for the transport equations using…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
We obtain a sharp limit H\"older continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under…
The Riemann solutions to Chaplygin Euler equations with a scaled pressure are considered. When the pressure vanishes, there are three cases. The Riemann solution containing two shock waves converges to the delta shock wave solution of the…
We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent developments averaging theory for ordinary differential…
We deal with the vanishing viscosity scheme for the transport/continuity equation $\partial_t u + \text{div }(u\boldsymbol{b} ) = 0$ drifted by a divergence-free vector field $\boldsymbol{b}$. Under general Sobolev assumptions on…
In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…
This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…
In the non viscous fluid dynamics, Smooth Particle Hydrodynamics (SPH), as a free Lagrangian "shock capturing" method adopts either an artificial viscosity contribution or an appropriate Riemann solver technique. An explicit or an implicit…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's problem in optimal…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
The paper aims on the construction of weak solutions to equations of a model of compressible viscous fluids, being a simplification of the classical compressible Navier-Stokes system. We present a novel scheme for approximating systems that…
Viscous streaming has emerged as an effective method to transport, trap, and cluster inertial particles in a fluid. Previous work has shown that this transport is well described by the Maxey-Riley equation augmented with a term representing…
This article addresses the local boundedness and H\"older continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and…
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…
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…