Global Solutions to the Generalized Leray- α System with Non- L²(Rⁿ) Initial Data

Due to the intractability of the Navier–Stokes equation, it is common to study approximating equations. Two of the most common of these are the Leray-α equation (which replaces the solution u with (1 - α²L₂) u for a Fourier Multiplier L₂) and the generalized Navier–Stokes equation (which replaces the viscosity term ν▵ with νL₁). In this paper, we use an interpolation based method to prove the existence of global solutions to the generalized Leray-α system with initial data in L^q(Rⁿ) for 2<q<2nn-2 with multipliers are of the form mi(ξ)=|ξ|γigi(|ξ|), where g is (essentially) a logarithm.