A Generalized Poisson--Nernst--Planck--Navier--Stokes Model on the Fluid with the Crowded Charged Particles: Derivation and Its Well-Posedness

DOI10.1137/16M1055104zbMath1416.35220OpenAlexW2520914149MaRDI QIDQ2821656

Yong Wang, Zhong Tan, Chun Liu

Publication date: 22 September 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1055104

zbMATH Keywords

well-posednesscross-diffusionenergetic variational approachPoisson-Nernst-Planck-Navier-Stokes equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items (16)

Existence of Solutions to the Poisson--Nernst--Planck System with Singular Permanent Charges in $\mathbb{R}^2$ ⋮ Stability of the nonconstant stationary solution to the Poisson-Nernst-Planck-Navier-Stokes equations ⋮ Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles ⋮ Dynamics of current, charge and mass ⋮ Green's function and pointwise estimate for a generalized Poisson‐Nernst‐Planck‐Navier‐Stokes model in dimension three ⋮ Quasi-neutral limit and the boundary layer problem of Planck-Nernst-Poisson-Navier-Stokes equations for electro-hydrodynamics ⋮ Global existence of the non-isothermal Poisson-Nernst-Planck-Fourier system ⋮ Global well-posedness of compressible magneto-micropolar fluid equations ⋮ On the Half-Space or Exterior Problems of the 3D Compressible Elastic Navier–Stokes–Poisson Equations ⋮ A linear, second-order accurate, positivity-preserving and unconditionally energy stable scheme for the Navier-Stokes-Poisson-Nernst-Planck system ⋮ Stability of the nonconstant stationary solution to the damped Poisson–Nernst–Planck–Euler equations ⋮ Global existence and long-time behavior of solutions to the full compressible Euler equations with damping and heat conduction in \(\mathbb{R}^3\) ⋮ Optimal decay rates of the solution for generalized Poisson-Nernst-Planck-Navier-Stokes equations in \(\mathbb{R}^3\) ⋮ Parabolic-elliptic system modeling biological ion channels ⋮ Optimal \(L^p\)-\(L^q\)-type decay rates of solutions to the three-dimensional nonisentropic compressible Euler equations with relaxation ⋮ Partial Regularity of Suitable Weak Solutions of the Navier--Stokes--Planck--Nernst--Poisson Equation

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