Existence and nonuniqueness

Two-dimensional Euler equations

\begin{array}{rcl} \partial_{t} u + div (u \otimes u) + \nabla p & = & 0, \\ div u & = & 0 . \end{array}

These equations describe the motion of an ideal fluid with velocity u(t, x) and pressure p(t, x), for x ∈ ℝ².

Here we collect AI-assisted manuscripts and their source material on the existence and nonuniqueness of weak solutions.

Delort’s question: sign-changing vortex-sheet data

A manuscript proposing global weak Euler solutions for arbitrary finite signed initial vorticity in H⁻¹, with a strong initial velocity trace and integrable vorticity at positive times.

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Non-unique vanishing-viscosity solutions of 2D Euler with vorticity in L^p

A manuscript proposing two distinct Euler solutions obtained as vanishing-viscosity limits from the same initial vorticity in L¹ ∩ L^p, for each 2 < p < ∞.

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Two-dimensional Euler equations

Delort’s question: sign-changing vortex-sheet data

Non-unique vanishing-viscosity solutions of 2D Euler with vorticity in Lp

Non-unique vanishing-viscosity solutions of 2D Euler with vorticity in L^p