Boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant

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Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “4 ([104], [9]) Let n ≥ 2 and Ω ⊂ R be a bounded domain with smooth boundary, and suppose that u0 and v0 satisfy (2.”
Analysis of a chemotaxis model with indirect signal absorption (2019, unknown): “In [1] this condition has then been improved; it is sufficient to require ‖v0‖L∞(Ω) < π √ 2(n+1) .”