Existence and uniqueness of a global weak solution of a Darcy-Nernst-Planck-Poisson system. (English) Zbl 1261.35121
Summary: This paper deals with the analytical investigations of a nonstationary Darcy-Nernst-Planck-Poisson-type system which is a mathematical model describing electrolyte solutions. For this nonlinear fully coupled system of partial differential equations we proof existence and uniqueness of global weak solutions. Furthermore, we establish physical properties for the number densities such as nonnegativity and boundedness in \(L^{\infty }((0, T) \times \Omega \)).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35D30 | Weak solutions to PDEs |
Keywords:
Darcy-Nernst-Planck-Poisson system; electro-hydrodynamics; Moser iteration; fixed point approach; global existenceReferences:
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