Mathematics of oil spills: existence, uniqueness, and stability of solutions

Abstract

An oil spill is modeled as a two-dimensional slick on a limited sea area when there is a nonzero oil flux through the open boundary. Conditions are suggested for the input and output parts of the domain boundary, and the unique solvability of the oil transport problem and its adjoint is proved for classes of generalized functions. It is also shown that solutions of the problem are stable in the presence of errors in the initial condition and in the oil emission rate from a damaged tanker. Direct and adjoint oil concentration estimates are suggested to evaluate the consequences of an accident involving oil spillage.