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math.AP2018
The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions
Diego Alonso-Orán, Aythami Bethencourt de León, So Takao
In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation a…
math-ph2018
Networks of Coadjoint Orbits: from Geometric to Statistical Mechanics
Alexis Arnaudon, So Takao
A class of network models with symmetry group that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenbe…