This chapter deals with the coarse scale velocity. It begins the proof of Lemma (10.1) by choosing a double mollification for the velocity field. Here ∈ᵥ is taken to be as large as possible so that higher derivatives of velement are less costly, and each vsubscript Element has frequency smaller than λ so elementv⁻¹ must be smaller than λ in order of magnitude. Each derivative of vsubscript Element up to order L costs a factor of Ξ. The chapter proceeds by describing the basic building blocks of the construction, the choice of elementv and the parametrix expansion for the divergence equation.
Quantum critical charge response from higher derivatives in holography