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<p>This paper investigates the initial-boundary value problem for the three-dimensional incompressible Hall-magnetohydrodynamics (Hall-MHD) system with ion-slip effect in a flat bounded domain. We establish the global existence of weak solutions and the local well-posedness of strong solutions in suitable Sobolev spaces. We derive uniform estimates independent of the fluid viscosity. Based on these estimates, we rigorously justify the vanishing viscosity limit, demonstrating that the solutions of the viscous system converge to those of the inviscid system as the viscosity coefficient tends to zero. Furthermore, we obtain an explicit convergence rate.</p>

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Well-Posedness and Vanishing Viscosity Limit of the 3D Hall-MHD System with Ion-Slip Effect in a Bounded Domain

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Zhendong Huang

摘要

This paper investigates the initial-boundary value problem for the three-dimensional incompressible Hall-magnetohydrodynamics (Hall-MHD) system with ion-slip effect in a flat bounded domain. We establish the global existence of weak solutions and the local well-posedness of strong solutions in suitable Sobolev spaces. We derive uniform estimates independent of the fluid viscosity. Based on these estimates, we rigorously justify the vanishing viscosity limit, demonstrating that the solutions of the viscous system converge to those of the inviscid system as the viscosity coefficient tends to zero. Furthermore, we obtain an explicit convergence rate.