Author

Ibrahim Suleiman

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Preprint Oct 2026

A well-posedness theory for the 2D inhomogeneous incompressible Euler equations and a class of global-in-time solutions

We consider the Cauchy problem for the 2D inhomogeneous incompressible Euler equations. We show that the Cauchy problem is locally well-posed in a class of $m$-fold symmetric functions at critical regularity and allowing the velocity field to grow linearly at spatial infinity. This was a problem posed by P.L. Lions in...

Ibrahim Suleiman · 0 citations

Preprint Sep 2026

Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations

Let $m \ge 4$. We prove that there is a forward orbit of the 2D Euler system for scale-invariant $m$-fold symmetric vorticities, namely \begin{equation*} \partial_tg + 2G\partial_\theta g = 0, \quad 4G + \partial_{\theta\theta}G = g, \end{equation*} which is dense in $S :=\{g \in L_{m,\mathrm{odd}}^\infty(\mathbb{S}^1)...

Ibrahim Suleiman · 0 citations