On correctors for linear elliptic homogenization in the presence of local defects: The case of advection–diffusion

Abstract We follow-up on our works devoted to homogenization theory for linear second-order elliptic equations with coefficients that are perturbations of periodic coefficients. We have first considered equations in divergence form in [6] , [7] , [8] . We have next shown, in our recent work [9] , using a slightly different strategy of proof than in our earlier works, that we may also address the equation − a i j ∂ i j u = f . The present work is devoted to advection–diffusion equations: − a i j ∂ i j u + b j ∂ j u = f . We prove, under suitable assumptions on the coefficients a i j , b j , 1 ≤ i , j ≤ d (typically that they are the sum of a periodic function and some perturbation in L p , for suitable p + ∞ ), that the equation admits a (unique) invariant measure and that this measure may be used to transform the problem into a problem in divergence form, amenable to the techniques we have previously developed for the latter case.