Global bounded weak solutions for a chemotaxis-Stokes system with nonlinear diffusion and rotation

Journal of Differential Equations ◽

10.1016/j.jde.2021.04.020 ◽

2021 ◽

Vol 289 ◽

pp. 182-235

Author(s):

Jiashan Zheng ◽

Yuanyuan Ke

Keyword(s):

Weak Solutions ◽

Nonlinear Diffusion ◽

Stokes System ◽

Bounded Weak Solutions

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Global weak solutions for the three-dimensional chemotaxis-Navier–Stokes system with nonlinear diffusion

Journal of Differential Equations ◽

10.1016/j.jde.2015.05.012 ◽

2015 ◽

Vol 259 (8) ◽

pp. 3730-3754 ◽

Author(s):

Qingshan Zhang ◽

Yuxiang Li

Keyword(s):

Weak Solutions ◽

Nonlinear Diffusion ◽

Stokes System ◽

Three Dimensional ◽

Navier Stokes ◽

Global Weak Solutions

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Global boundedness of weak solutions for a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and rotation

Journal of Differential Equations ◽

10.1016/j.jde.2019.11.072 ◽

2020 ◽

Vol 268 (11) ◽

pp. 7047-7091 ◽

Author(s):

Wei Wang

Keyword(s):

Weak Solutions ◽

Nonlinear Diffusion ◽

Stokes System ◽

Three Dimensional ◽

Global Boundedness

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Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with nonlinear diffusion

Journal of Differential Equations ◽

10.1016/j.jde.2017.04.005 ◽

2017 ◽

Vol 263 (5) ◽

pp. 2606-2629 ◽

Author(s):

Jiashan Zheng

Keyword(s):

Weak Solutions ◽

Nonlinear Diffusion ◽

Stokes System ◽

Three Dimensional ◽

Navier Stokes ◽

Global Weak Solutions

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Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-015-0922-2 ◽

2015 ◽

Vol 54 (4) ◽

pp. 3789-3828 ◽

Author(s):

Michael Winkler

Keyword(s):

Nonlinear Diffusion ◽

Stokes System ◽

Three Dimensional ◽

Large Time Behavior ◽

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GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION

Journal of the Korean Mathematical Society ◽

10.4134/jkms.2014.51.3.635 ◽

2014 ◽

Vol 51 (3) ◽

pp. 635-654 ◽

Author(s):

Yun-Sung Chung ◽

Kyungkeun Kang ◽

Jaewoo Kim

Keyword(s):

Global Existence ◽

Weak Solutions ◽

Nonlinear Diffusion ◽

Fluid Model ◽

Existence Of Weak Solutions

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Global existence of weak solutions for the anisotropic compressible Stokes system

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2020.04.003 ◽

2020 ◽

Vol 37 (6) ◽

pp. 1271-1297 ◽

Author(s):

D. Bresch ◽

C. Burtea

Keyword(s):

Global Existence ◽

Weak Solutions ◽

Stokes System ◽

Existence Of Weak Solutions

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Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system involving a tensor-valued sensitivity with saturation

Journal of Differential Equations ◽

10.1016/j.jde.2017.01.024 ◽

2017 ◽

Vol 262 (10) ◽

pp. 5271-5305 ◽

Author(s):

Ji Liu ◽

Yifu Wang

Keyword(s):

Weak Solutions ◽

Stokes System ◽

Three Dimensional ◽

Navier Stokes ◽

Global Weak Solutions

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Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2011.08.008 ◽

2012 ◽

Vol 386 (1) ◽

pp. 428-444 ◽

Author(s):

Pierluigi Colli ◽

Sergio Frigeri ◽

Maurizio Grasselli

Keyword(s):

Global Existence ◽

Weak Solutions ◽

Stokes System ◽

Navier Stokes ◽

Existence Of Weak Solutions

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Boundedness of weak solutions in a 3D chemotaxis-Stokes system with nonlinear doubly degenerate diffusion

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125545 ◽

2021 ◽

pp. 125545

Author(s):

Qingyun Lin

Keyword(s):

Weak Solutions ◽

Stokes System ◽

Degenerate Diffusion

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Local Hölder regularity for a doubly singular PDE

Communications in Contemporary Mathematics ◽

10.1142/s0219199718500542 ◽

2018 ◽

Vol 22 (03) ◽

pp. 1850054

Author(s):

Eurica Henriques

Keyword(s):

Parabolic Equation ◽

Weak Solutions ◽

Iteration Method ◽

Hölder Continuity ◽

Hölder Regularity ◽

Holder Continuity ◽

Singular Parabolic Equation ◽

Local Hölder Continuity ◽

Singular Pde ◽

Bounded Weak Solutions

We establish the local Hölder continuity for the nonnegative bounded weak solutions of a certain doubly singular parabolic equation. The proof involves the method of intrinsic scaling and the parabolic version of De Giorgi’s iteration method.

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