Unique solvability of the problem of impact with separation of a rigid body on a nonhomogeneous fluid. (Russian) Zbl 1299.76020

Yudovich, V. I.

Vladikavkaz. Mat. Zh. 7, No. 3, 79-88 (2005).

Summary: We study the motion of a fluid, which is caused by a blow on a solid floating in that fluid. The fluid is assumed to be incompressible and inhomogeneous. The problem reduces to a nonlinear mixed boundary value problem for the elliptic equation \(\text{div}\,(\frac1\rho\text{grad}\,\varphi)=0\), where \(\rho=\rho(x)\) is a given density, and \(\varphi\) is the impulsive pressure in the fluid. Using the technology of variational inequalities, we prove the existence and uniqueness of the generalized solution.

MSC:

76B07	Free-surface potential flows for incompressible inviscid fluids
35Q35	PDEs in connection with fluid mechanics

Keywords:

theory of elliptic problems; impact problem