Yulan Wang

TL;DR: For the case d = 3, a new method to establish the existence and boundedness of global classical solutions for arbitrarily large initial data under the assumption α > 1 2, which is slightly stronger than the corresponding subcritical assumption α> 1 3 on the fluid-free system as mentioned in this paper.

TL;DR: In this article, it was shown that the Stokes limit in a bounded convex domain with smooth boundary can stabilize to a given smooth potential, such that whenever the initial data are sufficiently smooth, the system will stabilize uniformly with respect to the time variable.

TL;DR: In this article, the degenerate Keller-Segel-Stokes system (KSS) was investigated in a bounded convex domain with smooth boundary, and it was shown that for any porous medium diffusion m>1, the KSS with nonnegative and smooth initial data possesses at least a global-in-time weak solution, which is uniformly bounded.

TL;DR: The chemotaxis-Stokes system is considered in this paper in a bounded domain Ω⊂R3 with smooth boundary and the corresponding solution theory is quite wel...

TL;DR: In this paper, the Keller-Segel-Stokes system is considered in a bounded domain with smooth boundary, with parameters ρ ≥ 0, μ > 0 and α > 1, and with a given gravitational potential Λ ∈ W2,∞(Ω).