Density large deviations for multidimensional stochastic hyperbolic conservation laws

Abstract

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the conductivity and dif-fusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in [4]. When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a general weak solution, and leave the general large deviation function upper bound as a conjecture.

References in corpus (5)

• Symmetries in Fluctuations Far from Equilibrium
• Order and symmetry-breaking in the fluctuations of driven systems
• Weak additivity principle for current statistics in d-dimensions
• A quasi-potential for conservation laws with boundary conditions
• Totally asymmetric limit for models of heat conduction

Cited by in corpus (4)

• Sampling rare events across dynamical phase transitions
• Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps