概要： In this talk I will present a local well-posedness result for a convective mean curvature flow equation coupled to a two-phase Navier–Stokes equation with surface tension in two and three dimensions. Using a Hanzawa-transform we write the equations as a nonlinear evolution equation for a height function over a fixed sharp interface coupled to a transformed two-phase Navier–Stokes equation on fixed domains. We solve the Navier–Stokes part in an $L^q$-setting for a given height function in suitable $L^p$-function spaces. For appropriate ranges of $p,q$ the contribution of the Navier–Stokes part in the evolution equation for the height function is of lower order. Then the latter can be solved with the theory of Maximal $L^p$-Regularity. To this end we use that the mean curvature has a quasilinear structure with respect to the height function.
This is joint work with Helmut Abels from Regensburg.
本セミナーは，東京理科大学 研究推進機構 総合研究院 「数理モデリングと数学解析研究部門」との共催です．
連絡先：梶原直人(kajiwara_naoto (at) ma.noda.tus.ac.jp,(at) を@に変えてお使いください.)