Related papers: Density large deviations for multidimensional stoc…
In this paper, we study the precise decay rate in time to solutions of the Cauchy problem for the one-dimensional conservation law with a nonlinearly degenerate viscosity where the far field states are prescribed. Especially, we deal with…
We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law. Our strategy relies on the…
The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting the conservation law only holds under the assumption that the…
By observing a new relation between the magnetic pressure and the hydrodynamic pressure, global existence of classical solution to the full perfect MHD equations with large data is established, in particular including the case when all the…
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? Our viscous term contains the…
The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place…
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions. In contrast to previous works, we…
We study the large deviations behavior of systems that admit a certain form of a product distribution, which is frequently encountered both in Physics and in various information system models. First, to fix ideas, we demonstrate a simple…
For periodic initial data with initial density allowed to vanish, we establish the global existence of strong and weak solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader…
Applying the concept of S-convergence, based on averaging in the spirit of Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler system are studied. We show how to efficiently compute a viscosity solution of the Euler…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
In this paper, we established the Freidlin-Wentzell type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
Stochastic density functional theory is applied to analyze the conductivity of strong two species electrolytes at arbitrary field strengths. The corresponding stochastic equations for the density of the electrolyte species are solved by…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic…