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<p>In this paper, we investigate the existence and uniqueness of mild solutions for a class of nonlinear Rayleigh-Stokes equations on the Heisenberg group in the fractional Sobolev space. Based on the expression of the mild solutions, we study the relevant properties of the solution operator. By utilizing the contraction mapping principle, we have successfully established the well-posedness of the mild solutions and the dependence on initial value.</p>

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Well-Posedness of the Nonlinear Fractional Rayleigh-Stokes Equations on the Heisenberg Group

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Xiaolin Liu,
  • Yong Zhou

摘要

In this paper, we investigate the existence and uniqueness of mild solutions for a class of nonlinear Rayleigh-Stokes equations on the Heisenberg group in the fractional Sobolev space. Based on the expression of the mild solutions, we study the relevant properties of the solution operator. By utilizing the contraction mapping principle, we have successfully established the well-posedness of the mild solutions and the dependence on initial value.