English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper studies the three-dimensional stochastic chemotaxis-Navier-Stokes(SCNS) system subjected to a L\'{e}vy-type random external force in boundeddomain. Up to now, the existing results concerning global solvability of SCNSsystem mainly concentrated on the case of two spacial dimensions, little isknown for the SCNS system in dimension three. We prove in present work that thethree-dimensional SCNS system possesses at least one global martingale solutionunder proper assumptions, which is weak both in the analytical sense and in thestochastic sense. A new stochastic analogue of entropy-energy inequality and anuniform boundedness estimate are derived, which enable us to constructglobal-in-time approximate solutions from a properly regularized SCNS systemvia the Contraction Mapping Principle. The proof of the existence of martingalesolution is based on the stochastic compactness method and an elaborateidentification of the limits procedure, where the Jakubowski-Skorokhod Theoremis applied to deal with the phase spaces equipped with weak topology.

Global martingale weak solutions for the three-dimensional stochastic chemotaxis-Navier-Stokes system with L\'{e}vy processes