On the interaction between compressible inviscid flow and an elastic plate
Igor Kukavica\v{S}\'arka Ne\v{c}asov\'aAmjad Tuffaha
Igor Kukavica\v{S}\'arka Ne\v{c}asov\'aAmjad Tuffaha
Nov 2023
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摘要原文
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the interaction of an inviscid fluid with an elastic plate. We establish a priori estimates on local-in-time solutions in low regularity Sobolev spaces, namely with velocity and density initial data v0,R0 in H3. The main new device is a variable coefficients space tangential-time differential operator of order 1 with non-homogeneous boundary conditions, which captures the hyperbolic nature of the compressible Euler equations as well as the coupling with the structural dynamics.
