Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with a conservation law

Abstract. Hydrodynamic limit for the Ginzburg-Landau ∇φ in-terface model was established in [5] under the periodic boundary con-ditions. This paper extends their results to the modified dynamics which preserve the total volume of each microscopic phase. Nonlinear partial differential equation of fourth order ∂h ∂t = − ∆ [div {(∇σ)(∇h(t, θ))}] , θ ∈ Td ≡ [0, 1)d, t> 0 is derived as the macroscopic equation, where σ = σ(u) is the surface tension of the surface with tilt u ∈ Rd. The main tool is H−2-method, which is a modification of H−1-method used in [5]. The Gibbs mea-sures associated with the dynamics are characterized. 1