Speaker
Description
In this talk, I will report a recent work on the sharp interface limit of a Navier--Stokes/Allen--Cahn system as the interfacial thickness $\varepsilon$ tends to zero for well-prepared initial data as long as the limit system possesses a sufficiently smooth solution. We propose a systematic argument based on the linearization of the errors. The convergence results relies crucially on uniform higher-order estimates for the associated linearized Navier--Stokes/Allen--Cahn system in suitably weighted $L^2$-Sobolev spaces. Here a novel problem-adapted weight proportional to the sum of ε and the distance to the sharp interface of the limit, which gives improved and sharp estimates, is an important new ingredient. This approach can be potentially adapted to other sharp interface limits as well.