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 Lq(Rn) for 2<q<2nn-2 with multipliers are of the form mi(ξ)=|ξ|γigi(|ξ|), where g is (essentially) a logarithm.
|Original language||English (US)|
|Number of pages||15|
|Journal||Journal of Dynamics and Differential Equations|
|State||Published - Sep 1 2020|
All Science Journal Classification (ASJC) codes