Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (6): 1789-1802.

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The Well-posedness of a Delayed Non-Newtonian Fluid on ${2D}$ Unbounded Domains

Liu Guowei*(),Wang Qiling()   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
  • Received:2022-11-07 Revised:2023-03-02 Online:2023-12-26 Published:2023-11-16
  • Supported by:
    NSFC(12001073);NSF of Chongqing(cstc2020jcyj-msxmX0709);Science and Technology Research Foundation of Chongqing Education Commission(KJQN201900563)

Abstract:

In this paper, we study the well-poseness of a non-autonomous delayed incompressible non-Newtonian fluid on $2D$ unbounded domains. With a minimal regularity of the force, we prove the existence of solutions by the method of combining the technique of domain decomposition with the Garlerin approximation. Then we use the energy method to prove the uniqueness and the stability of solutions.

Key words: Non-Newtonian fluid, Delay, Well-posedness

CLC Number: 

  • O373
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