On the local and global existence of solutions to 1D transport equations with nonlocal velocity

Hantaek Bae; Rafael Granero-Belinchón; Omar Lazar

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arXiv · 1806.01011

On the local and global existence of solutions to 1D transport equations with nonlocal velocity

Hantaek Bae·Rafael Granero-Belinchón·Omar Lazar

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Abstract

We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &\theta_t+u\theta_x+\nu \Lambda^{\gamma}\theta=0, \\ & u=\mathcal{N}(\theta), \end{split} \end{equation*} where $\mathcal{N}$ is a nonlocal operator. In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators.

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Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar. 2018-06-04. On the local and global existence of solutions to 1D transport equations with nonlocal velocity. https://arxiv.org/abs/1806.01011

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