Global Solutions Of The Nernst-Planck-Navier-Stokes Equations With Blocking Boundary Conditions

In this thesis,we consider the Nernst-Planck-Navier-Stokes(NPNS)equations for simulating ion electrodiffusion problems in fluids,and prove the global well-posedness of strong solution of Nernst-Planck-Navier-Stokes(NPNS)equations on two-dimensional bounded domain.Where the ionic concentration with the inhomogeneous blocking(vanishing normal flux)boundary condition,the electric potential has a homogeneous Neumann boundary condition,and the fluid velocity has a homogeneous Dirichlet boundary condition.And we assume that the ion species of the equations are divided into two cases: one is that there are only two kinds of ions,the other is that for any number of ions,all diffusion coefficients are equal and the absolute value of valence is the same.Under all the above assumptions,the proof process in this thesis is as follows: Firstly,the existence and uniqueness of the local solutions of the NPNS equations are proved by using the principle of compression mapping.Secondly,the priori estimates of the solutions are obtained by using the energy estimates of elliptic and parabolic equations,and the regularity theory is used to improve the priori estimates,which are the key to prove the global solutions.Finally,according to the local solution conclusions and priori estimates,the obtained local solutions are extended to the whole time by using the method of inverse proof.In this thesis,we use the principle of contraction mapping,the energy estimates,and the regularity theory of elliptic and parabolic equations.