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 --aij$\partial$iju = f. The present work is devoted to advection-diffusion equations: --aij$\partial$iju + bj$\partial$ju = f. We prove, under suitable assumptions on the coefficients aij, bj, 1 $\le$ i, j $\le$ d (typically that they are the sum of a periodic function and some perturbation in L p , for suitable p < +$\infty$), 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.