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- W4292691990 abstract "Abstract In this article, we will develop an analytical approach to construct the global bounded weak solutions to the initial-boundary value problem of a three-dimensional chemotaxis-Stokes system with porous medium cell diffusion <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=normal>Δ</m:mi> <m:msup> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>m</m:mi> </m:mrow> </m:msup> </m:math> Delta {n}^{m} for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>m</m:mi> <m:mo>≥</m:mo> <m:mfrac> <m:mrow> <m:mn>65</m:mn> </m:mrow> <m:mrow> <m:mn>63</m:mn> </m:mrow> </m:mfrac> </m:math> mge frac{65}{63} and general sensitivity. In particular, this extended the precedent results which asserted global solvability within the larger range <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>m</m:mi> <m:mo>></m:mo> <m:mfrac> <m:mrow> <m:mn>7</m:mn> </m:mrow> <m:mrow> <m:mn>6</m:mn> </m:mrow> </m:mfrac> </m:math> mgt frac{7}{6} for general sensitivity (M. Winkler, Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity, Calc. Var. 54 (2015), 3789–3828) or <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>m</m:mi> <m:mo>></m:mo> <m:mfrac> <m:mrow> <m:mn>9</m:mn> </m:mrow> <m:mrow> <m:mn>8</m:mn> </m:mrow> </m:mfrac> </m:math> mgt frac{9}{8} for scalar sensitivity (M. Winkler, Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement, J. Differ. Equ. 264 (2018), 6109–6151). Our proof is based on a new observation on the quasi-energy-type functional and on an induction argument." @default.
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- W4292691990 date "2022-08-19" @default.
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- W4292691990 title "Global boundedness to a 3D chemotaxis-Stokes system with porous medium cell diffusion and general sensitivity" @default.
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- W4292691990 doi "https://doi.org/10.1515/anona-2022-0228" @default.
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