Global regularity of multi-dimensional Burgers equation with critical dissipation only in one direction

In this paper, we are concerned with the multi-dimensional Burgers equation with the critical dissipation only in one direction. We make use of the elegant method introduced by Constantin and Vicol to show the unique global existence of smooth solution.

Keywords

multi-dimensional Burgers equation, global regularity, critical dissipation

2010 Mathematics Subject Classification

Primary 35B65, 35Q35, 76D05. Secondary 35Q53.

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The author acknowledges support from the Qing Lan Project of Jiangsu Province, and thanks for hospitality the School of Mathematical Sciences, Beijing Normal University, where part of this work was carried out.

Received 19 September 2022

Published 1 November 2023