Local existence for variable-coefficient 3D Euler at optimal regularity r>2.5, plus a BKM blow-up criterion at r=3 involving BMO vorticity and H1 velocity.
A free boundary inviscid model of flow-structure interaction
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abstract
We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a~priori estimates for the existence with the optimal regularity $H^{r}$, for $r>2.5$, on the fluid initial data and construct a unique solution of the system for initial data $u_0\in H^{r}$ for $r\geq3$. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur.
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The Euler equations with variable coefficients
Local existence for variable-coefficient 3D Euler at optimal regularity r>2.5, plus a BKM blow-up criterion at r=3 involving BMO vorticity and H1 velocity.