An $$L^2$$ approach to viscous flow in the half space with free elastic surface

Abstract We consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in half space $${\mathbb {R}}^n_+$$ R + n such that on lower boundary function h satisfying undamped Kirchhoff-type plate equation is coupled to field. Originally, describes height underlying nonlinear free surface problem. Since contains no damping term, this article uses $$L^2$$ L 2 -theory yielding existence strong solutions finite time intervals framework homogeneous Bessel potential spaces. The proof based -Fourier analysis and also deals with inhomogeneous data velocity field “free boundary” $$x_n=0$$ x = 0 .