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<p>This paper addresses the <i>n</i>–dimensional Stokes and Navier–Stokes systems in a non-cylindrical domain. The main results establish null and approximate controllability with internal controls supported in potentially small subdomains. First, we study the systems by transforming them into an equivalent system defined in a cylinder and then we solve the corresponding control problems (null controllability is achieved under a restriction on the transformation). In our approach, we employ a Carleman inequality for the Stokes system with variable coefficients. In the nonlinear case, we also apply Liusternik’s Inverse Mapping Theorem.</p>

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Null and Approximate Controllability for the Stokes System and Local null Controllability for the Navier–Stokes System in a Non-Cylindrical Domain

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • L. Cipriano,
  • J. Límaco,
  • A. T. Lourêdo,
  • M. Milla Miranda,
  • P. Queiroz–Souza

摘要

This paper addresses the n–dimensional Stokes and Navier–Stokes systems in a non-cylindrical domain. The main results establish null and approximate controllability with internal controls supported in potentially small subdomains. First, we study the systems by transforming them into an equivalent system defined in a cylinder and then we solve the corresponding control problems (null controllability is achieved under a restriction on the transformation). In our approach, we employ a Carleman inequality for the Stokes system with variable coefficients. In the nonlinear case, we also apply Liusternik’s Inverse Mapping Theorem.