Optimal Control Of Coupled Oil-water-surfactant And Navier-Stokes System

In this thesis,we first studied the high order equation of CH-NS the initial-boundary value problem.By the discretization equations and energy estimate,we proved the existence of the problem,and gave the optimal control of the problem.The correlative adjoint systems are also discussed and the correlative conclusions are given.Second,we studied the initial boundary value problem for the coupling of the oil,water,surfactant and Navier-Stokes equations:where f(c)=F(c),F(c)=(c+1)2(c2+h0)(c-1)2,a(c)=a2c2+a0,?(?)Rn,n=2,3,is a bounded domain with smooth boundary,and n is the outer normal vector of(?)?.By the similar discretization of the system,we obtained the existence of the solution.At the same time,we proved the existence of the optimal solution by establishing a new functional.