Title: Vanishing capillarity limit of a generic compressible two-fluid model with common pressure
Abstract: We investigate vanishing capillarity limit problem of a generic compressible two-fluid model with common pressure (P+=P-) in R3. Due to partial dissipation property of the system and strong coupling effects between two fluids, up to now, the vanishing capillarity limit of the 3D compressible two-fluid model with common pressure has remained a challenging problem.In the present work, by exploiting the dissipation structure of the model and employing several key observations, we show that the unique smooth solution of the generic compressible two-fluid model exists for all time, and converges globally in time to the unique smooth solution of the compressible two-fluid Navier-Stokes equations, as the capillary coefficient σ tends to zero. Moreover, as a by-product, we also obtain the convergence rate estimates with respect to the capillary coefficient σ for any given positive time.
姚磊，西北工业大学教授，2010年在华中师范大学获理学博士学位。主要从事流体力学中的偏微分方程数学理论的研究，论文发表在 Math. Ann.、JMPA、Ann. I. H. Poincaré -AN、SIAM JMA、Indiana Univ. Math. J.、M3AS等国际期刊上。