The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties

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Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “4 ([128], [11], [143]) Let Ω ⊂ R2 be a bounded domain with smooth boundary, and assume (3.”
Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion (2016, background): “Solutions emanating from large data, however, have not been proven to be bounded and might blow up and cease to exist as classical solutions after a finite time, continuing only as generalized solutions in the sense of [43].”
Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D (2017, methodology): “In this setting, building on the work [38], it was shown in [30] that for any (n0, c0, u0) satisfying (1.”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, methodology): “The use of such functionals with sublinear growth with respect to the unknown seems rather unusual in the context of cross-diffusive systems of the considered class, especially when intended to be a starting point of a series of arguments finally resulting in boundedness and smoothness of solutions;”