Nonlinear inviscid damping near monotonic shear flows
Alexandru D. Ionescu, Hao Jia
Abstract
jia Energy functionals and the bootstrap propositionThe main idea of the proof is to estimate the increment of suitable energy functionals, which are defined using special weights.For simplicity, we use exactly the same weights A N R , A R , and A k , as in our earlier papers [20] and[21], so we can use some of their properties proved there.These weights are defined by and HIn this subsection, we prove the following bounds.Proposition 5.1.With the definitions and assumptions in Proposition 2.2, we haveThe rest of the subsection is concerned with the proof of this proposition.The arguments are similar to the arguments in [20, §6], and we will be somewhat brief.non-linear inviscid damping near monotonic shear flows 363 Using definitions (2.46) and (2.47), we calculate d dt g∈{H,V ′ * ,B ′ * ,B ′′