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
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• 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.