On the Navier-Stokes equations

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Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system (2015, background): “For α ∈ (0, 1), we let A denote the corresponding closed fractional power of A [19].”
On optimal initial value conditions for local strong solutions of the Navier–Stokes equations (2009, background): “Since then there have been developed several sufficient initial value conditions for the existence of local strong solutions, getting weaker step by step and enlarging the corresponding solution class, see [9,12,14,16,18,20,21,23], and the recent results in [2].”
Stability and convergence of efficient Navier‐Stokes solvers via a commutator estimate (2007, unknown): “[Soh]).”
On large deviations of coupled diffusions with time scale separation (2013, background): “loc(R l,Rl). Therefore, R Rl Φs,ms(·),u(x) T f(x)dx = 0. It follows that Φs,m s(·),u(x) = Dw˜s(u,x) in the sense of distributions, where ˜ws(u,·) ∈ L2 loc(R l), see, e.g., Lemma 2.2.1 on p.73 in Sohr [47]. Consequently, R Rl χ(x) T Φ s,ms(·),u(x)dx= − R Rl divχ(x) ˜ws(u,x)dx, for all χ∈ C10(Rl,Rl). ”