2017/02/28 by Julien Barré, Cédric Bernardin, Cedric Bernardin +2
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Conjecture #Conservation law #Fluid Dynamics and Turbulent Flows #Function (biology) #Large deviations theory #Limit (mathematics) #Limit of a function #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Probability density function #Pure mathematics #Quantum mechanics #Rate function #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Thermal diffusivity #Upper and lower bounds #cond-mat.stat-mech #math.PR
paper · pdf · doi:10.1007/s10955-017-1935-3
openalex created_date 2017/06/15 · arxiv created 2017/08/16 · openalex publication_date 2017/12/07 · arxiv updated 2018/03/14 · openalex updated_date 2026/08/05
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.