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arXiv · 2608.01806

The Burgers' Equation in the Hermite-Sobolev Spaces

Suprio Bhar·Rajeev Bhaskaran·Barun Sarkar
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Abstract

In this paper, we show existence and uniqueness of solutions to the viscous Burgers' equation in $\mathbb{R}^d$, when the initial condition $u_0$ is in Hermite-Sobolev space of index $p$, for suitable non-negative integers $p$. Our solutions are local in time. We also have a regularity result, viz. if $u_0$ belongs to Schwartz space, then so does the solution.

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Suprio Bhar, Rajeev Bhaskaran, Barun Sarkar. 2026-08-03. The Burgers' Equation in the Hermite-Sobolev Spaces. https://arxiv.org/abs/2608.01806

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