| Abstract: |
| We obtain the local existence and uniqueness of solutions 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 $r\geq3$.
We also address the compressible Euler equations in a domain with a free elastic boundary, evolving according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure.
We establish a~priori estimates on local-in-time solutions in low regularity Sobolev spaces, namely with velocity and density initial data
%$v_{0}, R_{0}$
in~$H^{3}$. This is joint work with Igor Kukavica and Sarka Necasova. |
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