Energy-type estimates and global solvability in a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant

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The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, unknown): “3 into κ-independent global estimates for ∫ n p and ∫ |∇c|2p with arbitrary p > 1, we shall make use of the following special case of a more general Gagliardo–Nirenberg-type interpolation inequality [31] which can be proved by straightforward adaptation of the argument introduced in [3].”
Global classical solution and boundedness to a chemotaxis‐haptotaxis model with re‐establishment mechanisms (2018, methodology): “Using a fixed point argument similar to [19], we can obtain the following local existence result of classical solution to (3.”