Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
George Avalos, Irena Lasiecka, Roberto Triggiani ยท Georgian Mathematical Journal ยท 2008
Abstract This paper considers an established model of a parabolic-hyperbolic coupled system of two PDEs, which arises when an elastic structure is immersed in a fluid. Coupling occurs at the interface between the two media. Semigroup well-posedness on the space of finite energy for {๐ค, ๐ค ๐ก , ๐ข} was established in [Contemp. Math. 440: 15โ54, 2007]. Here, [๐ค, ๐ค ๐ก ] are the displacement and the velocity of the structure, while ๐ข is the velocity of the fluid. The domain D ( A ) of the generator A does not carry any smoothing in the ๐ค-variable (its resolvent ๐ (ฮป, A ) is not compact on this component space). This raises the issue of higher regularity of solutions. This paper then shows that the mechanical displacement, fluid velocity, and pressure terms do enjoy a greater regularity if, in addition to the I.C. {๐ค 0 , ๐ค 1 , ๐ข 0 } โ D ( A ), one also has ๐ค 0 in (๐ป 2 (ฮฉ ๐ )) ๐ .