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The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions by Alonso-Orán, Diego; de León, Aythami Bethencourt; Takao, So is a scholarly article available to read on EtoBox.

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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 and then obtain a stochastic Rankine-Hugoniot condition that the shocks satisfy. Next, we establish the local existence and uniqueness of smooth solutions in the inviscid case and construct a blow-up criterion. Finally, in the viscous case, we prove global existence and uniqueness of smooth solutions.

Author

Alonso-Orán, Diego; de León, Aythami Bethencourt; Takao, So

Published

2018

Language

EN