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Global strong solution for the stochastic tamed Chemotaxis–Navier–Stokes system in R3

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  • Xu, Fan
  • Zhang, Lei
  • Liu, Bin

Abstract

In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier–Stokes equations (STCNS, for short). Our main goal is to establish the existence and uniqueness of a global strong solution (strong in both the probabilistic and PDE senses) for the 3D STCNS system with large initial data. To achieve this, we first introduce a triple approximation scheme by using the Friedrichs mollifier, frequency truncation operators, and cut-off functions. This scheme enables the construction of sufficiently smooth approximate solutions and facilitates the effective application of the entropy-energy method. Then, based on a newly derived stochastic version of the entropy-energy inequality, we further establish some a priori higher-order energy estimates, which together with the stochastic compactness method, allow us to construct the strong solution for the STCNS system.

Suggested Citation

  • Xu, Fan & Zhang, Lei & Liu, Bin, 2025. "Global strong solution for the stochastic tamed Chemotaxis–Navier–Stokes system in R3," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001759
    DOI: 10.1016/j.spa.2025.104732
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    References listed on IDEAS

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    1. Hausenblas, Erika & Moghomye, Boris Jidjou & Razafimandimby, Paul André, 2024. "On the existence and uniqueness of solution to a stochastic Chemotaxis–Navier–Stokes model," Stochastic Processes and their Applications, Elsevier, vol. 170(C).
    2. Mimura, Masayasu & Tsujikawa, Tohru, 1996. "Aggregating pattern dynamics in a chemotaxis model including growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 499-543.
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