Sharp interface limit of the convective Allen-Cahn equation in high dimensional spaces

In this manuscript, we analyze the convective Allen-Cahn equation with a vanishing mobility mɛ = ɛ. Given a smooth divergence-free velocity field and well-prepared initial data, the corresponding sharp interface limit is derived in a rigorous manner of matched asymptotic expansions as the thickness of the diffuse interface tends to 0. This extends the result in Abels, “Convergence of a convective Allen-Cahn equation to a transport equation,” arXiv:2401.02807 (2024) to high dimensional spaces.