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<p>This article is concerned with the inflow problem of the bipolar quantum Navier-Stokes-Poisson system in one dimension. By exploiting center manifold theory, we first establish the existence of stationary waves with spatial decay rate provided the boundary strength is small enough. Finally using energy estimates and Poincaré type inequalities, we obtain the asymptotic stability of stationary wave under smallness assumption of initial and boundary data.</p>

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Stability of stationary solutions to the inflow problem for the bipolar quantum Navier-Stokes-Poisson system

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Balakrishna Chhatria,
  • T. Raja Sekhar

摘要

This article is concerned with the inflow problem of the bipolar quantum Navier-Stokes-Poisson system in one dimension. By exploiting center manifold theory, we first establish the existence of stationary waves with spatial decay rate provided the boundary strength is small enough. Finally using energy estimates and Poincaré type inequalities, we obtain the asymptotic stability of stationary wave under smallness assumption of initial and boundary data.