We introduce the concept of strong null condition and discovered that incompressible fluid PDEs inherently satisfy such a condition. Analytically such a structure plays a crucial role in imporving the time decay rate of good unknowns. As a consequence, we are able to prove the global stability of incompressible elastodynamics in two dimensions which was a long-standing open question (Lei, 2016). Moreover, such a structure is also revealed to be crucial in the study of global vanishing viscosity limit. This is a key topics in both the theory of fluid mechanics and the analysis of partial differential equations. In general, as long as the time is global, the verification of such a theory is highly nontrivial and is thus open for most fluid systems. In the second part, we report our recent results on the global vanishing limit of incompressible viscoelasticity (joint with Yuan Cai, Fanghua Lin and Nader Masmoudi, preprint) and MHD (joint with Yuan Cai, 2018).