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The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

  • Li Peng [1] ; Yong Zhou [2]
    1. [1] Xiangtan University

      Xiangtan University

      China

    2. [2] Macau University of Science and Technology

      Macau University of Science and Technology

      RAE de Macao (China)

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper, we prove a long time existence result for fractional Rayleigh-Stokes equations derived from a non-Newtonain fluid for a generalized second grade fluid with memory. More precisely, we discuss the existence, uniqueness, continuous dependence on initial value and asymptotic behavior of global solutions in Besov-Morrey spaces.

      The proof is based on real interpolation, resolvent operators and fixed point arguments.

      Our results are formulated that allows for a larger class in initial value than the previous works and the approach is also suitable for fractional diffusion cases.


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