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Global Existence of Large Solutions for the 3D incompressible Navier--Stokes--Poisson-- Nernst--Planck Equations
  • Jihong Zhao,
  • Ying Li
Jihong Zhao
Baoji University of Arts and Sciences

Corresponding Author:jihzhao@163.com

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Ying Li
Baoji University of Arts and Sciences
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Abstract

This work is concerned with the global existence of large solutions to the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible Navier–Stokes–Poisson–Nernst–Planck equations. Making full use of the algebraic structure of the system, we obtain the global existence of solutions without smallness assumptions imposed on the third component of the initial velocity field and the summation of initial densities of charged species. More precisely, we prove that there exist two positive constants c 0 , C 0 such that if the initial data satisfies ( ∥ u 0 h ∥ B _ p , 1 − 1 + 3 p + ∥ N 0 − P 0 ∥ B _ q , 1 − 2 + 3 q ) exp { C 0 ( ∥ u 0 3 ∥ B _ p , 1 − 1 + 3 p 2 + ( ∥ N 0 + P 0 ∥ B _ r , 1 − 2 + 3 r + 1 ) exp { C 0 ∥ u 0 3 ∥ B _ p , 1 − 1 + 3 p } + 1 ) } ≤ c 0 , then the incompressible Navier–Stokes–Poisson–Nernst–Planck equations admits a unique global solution.
21 Nov 2022Submitted to Mathematical Methods in the Applied Sciences
21 Nov 2022Submission Checks Completed
21 Nov 2022Assigned to Editor
28 Nov 2022Review(s) Completed, Editorial Evaluation Pending
29 Nov 2022Reviewer(s) Assigned
06 Sep 2023Editorial Decision: Revise Minor
07 Sep 20231st Revision Received
11 Sep 2023Submission Checks Completed
11 Sep 2023Assigned to Editor
11 Sep 2023Review(s) Completed, Editorial Evaluation Pending
12 Sep 2023Reviewer(s) Assigned
08 Oct 2023Editorial Decision: Accept