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arXiv · 1609.03231

On the $L^p$ regularity of solutions to the generalized Hunter-Saxton system

Jaeho Choi·Nitin Krishna·Nicole Magill·Alejandro Sarria
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Abstract

The generalized Hunter-Saxton system comprises several well-known models from fluid dynamics and serves as a tool for the study of fluid convection and stretching in one-dimensional evolution equations. In this work, we examine the global regularity of periodic smooth solutions of this system in $L^p$, $p \in [1,\infty)$, spaces for nonzero real parameters $(\lambda,\kappa)$. Our results significantly improve/extend those by Wunsch et al. [27-29] and Sarria [21]. Furthermore, we study the effects that different boundary conditions have on the global regularity of solutions by replacing periodicity with a homogeneous three-point boundary condition and establish finite-time blowup of a local-in-time solution of the resulting system for particular values of the parameters.

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Jaeho Choi, Nitin Krishna, Nicole Magill, Alejandro Sarria. 2016-09-11. On the $L^p$ regularity of solutions to the generalized Hunter-Saxton system. https://arxiv.org/abs/1609.03231

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