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math.AP2022
The inviscid limit of viscous Burgers at nondegenerate shock formation
Sanchit Chaturvedi, Cole Graham
We study the vanishing viscosity limit of the one-dimensional Burgers equation near nondegenerate shock formation. We develop a matched asymptotic expansion that describes small-vi…
math.AP2021
Phase mixing for solutions to 1D transport equation in a confining potential
Sanchit Chaturvedi, Jonathan Luk
Consider the linear transport equation in D under an external confining potential : \begin{equation*} \partial_t f + v \partial_x f - \partial_x Φ\partial_v f = 0. \end{equat…
math.AP2019
Local existence for the Landau Equation with hard potentials
Sanchit Chaturvedi
We consider the spatially inhomogeneous Landau equation with hard potentials (i.e. with ) on the whole space . We prove existence and uniquenss of solutio…