Advances in Differential Equations

Strong solutions for a fluid structure interaction system

Igor Kukavica, Amjad Tuffaha, and Mohammed Ziane

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We consider the structure-interaction model, introduced by J.-L. Lions, describing the interaction of an elastic body and an incompressible fluid. Recently, many works have addressed well posedness for this model. In this paper, we prove local existence of strong solutions under the initial condition $(u_0,w_0,w_1)\in H^{1}\times H^{3/2+k}\times H^{1/2+k}$ for every $k>0$ sufficiently small and where $u_0$, $w_0$, and $w_1$ are the initial velocity of the fluid, initial displacement of the body, and the initial velocity of the body respectively. We also propose new alternative matching stress boundary conditions for this model.

Article information

Adv. Differential Equations, Volume 15, Number 3/4 (2010), 231-254.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30] 35K55: Nonlinear parabolic equations 35K15: Initial value problems for second-order parabolic equations


Kukavica, Igor; Tuffaha, Amjad; Ziane, Mohammed. Strong solutions for a fluid structure interaction system. Adv. Differential Equations 15 (2010), no. 3/4, 231--254.

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