Global Existence and Decay Rates of Large Solutions for the 3D Incompressible Dissipative System Modeling Electrohydrodynamics

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ABSTRACT In this paper, we are concerned with global existence and temporal decay rates of large solutions for a mathematical model arising from electrohydrodynamics (EHD), which is the nonlinear dissipative system coupled by the Poisson‐Nernst‐Planck equations and the incompressible Navier‐Stokes equations through charge transport and external forcing terms. By introducing a proper weighted function based on carefully examining the algebraic structure of the system, we prove that there exist two positive constants such that if the initial data satisfies then the system admits a unique global solution, where , and denotes the heat flow. In addition, by using the weighted Chemin‐Lerner type norm and interpolation techniques, we establish the optimal temporal decay rates of these global large solutions.

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