The authors construct case (c) least-total-curvature steady Euler flows in a strip and stable monotone semilinear solutions with non-convex superlevel sets.
Traveling waves near Poiseuille flow for the 2D Euler equation
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In this paper we reveal the existence of a large family of new, nontrivial and Lipschitz traveling waves for the 2D Euler equation at an arbitrarily small distance from the Poiseuille flow in $H^s$, with $s<3/2$, at the level of the vorticity.
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Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
The authors construct case (c) least-total-curvature steady Euler flows in a strip and stable monotone semilinear solutions with non-convex superlevel sets.