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Global existence of weak solutions for 2D chemotaxis-Navier-Stokes system with fractional diffusion
  • Jijie Zhao,
  • Xiaoyu Chen,
  • Qian Zhang
Jijie Zhao
Hebei University
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Xiaoyu Chen
Hebei University
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Qian Zhang
Hebei University

Corresponding Author:[email protected]

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Abstract

In this paper, we consider the following 2D incompressible chemotaxis-Navier-Stokes equations with the fractional diffusion { ∂ t n + u · ∇ n − ∆ n = − ∇ · ( n ∇ c )+ n ( 1 − n )( n − a ) , ∂ t c + u · ∇ c − ∆ c = − cn , ∂ t u + u · ∇ u + ∧ 2 α u + ∇ P = − n ∇ ϕ , where ∧ : = ( − ∆ ) 1 2 and α ∈ [ 1 2 , 1 ] . By establishing the new priori estimates, we get the global well-posedness for the above system with large initial data.
27 Mar 2024Submitted to Mathematical Methods in the Applied Sciences
17 Apr 2024Reviewer(s) Assigned
13 Jul 2024Review(s) Completed, Editorial Evaluation Pending
19 Jul 2024Editorial Decision: Revise Minor
29 Jul 20241st Revision Received
30 Jul 2024Submission Checks Completed
30 Jul 2024Assigned to Editor
30 Jul 2024Review(s) Completed, Editorial Evaluation Pending
01 Aug 2024Reviewer(s) Assigned
09 Aug 2024Editorial Decision: Revise Minor
16 Aug 20242nd Revision Received
19 Aug 2024Submission Checks Completed
19 Aug 2024Assigned to Editor
19 Aug 2024Review(s) Completed, Editorial Evaluation Pending
26 Aug 2024Reviewer(s) Assigned
14 Oct 2024Editorial Decision: Accept