Solutions and Drift Homogenization for a Class of Viscous Lake Equations in L2 (Ω)

In this paper, we study solutions and drift homogenization for a class of viscous lake equations using the method of semigroups of bounded operators. Suppose that the initial value ( t 0 ,u 0 ) ∈ U , i.e., u 0 = u(t 0 ) , for some Hölder continuous function u on [ 0,T ] with smooth function value u(t) ∈ DL 2 (Ω) 1/2 satisfying ∂ j u i = 0(i ≠ j) and b(x) ∈ C ∞ (Ω) . Then, the initial value problem for viscous lake equations has a unique smooth local strong solution. Using this result, we study the drift homogenization for the three-dimensional stationary Stokes equation in the usual sense, bDL 2 (Ω) . Mathematics Subject Classification (2010). Primary 35Q30, 35B27; Secondary 76N10, 76M50, 47D06.