报告时间：2026年5月11日（周一）下午 14:00-15:00

线上报告：腾讯会议 714-353-438

报告人：黄祥娣 研究员，中国科学院

报告摘要：

In this talk, we first prove the existence of global classical solutions to the 3D compressible quantum Navier-Stokes equations for general initial data. This result marks the first proof of global classical solutions with arbitrarily large initial data for a physically meaningful three-dimensional fluid equation in the history of compressible fluid mechanics. In order to achieve that, we develop a new Nash-Moser iteration method to derive the upper and lower bound of the density, which is expected to be widely applicable for improving $L^p$ integrability to $L^\infty$ regularity for general parabolic equations. Building on this observation, we further establish the existence of global classical solutions to the 3D general compressible Navier-Stokes-Korteweg equations with arbitrarily large initial data, thereby resolving a long-standing open problem which was originally proposed by the Dutch mathematician Korteweg in 1901 and later rigorously formulated by Dunn and Serrin in 1985.

邀请人：王云