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

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 نشر من قبل Hantaek Bae
 تاريخ النشر 2018
  مجال البحث
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We consider the 1D transport equation with nonlocal velocity field: begin{equation*}label{intro eq} begin{split} &theta_t+utheta_x+ u 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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