Mathematical Analysis of Navier-Stokes Equations and Related Models

ISBN-13: 9783659556340 / Angielski / Miękka / 2014 / 220 str.

Zhang Yinghui;Tan Zhong

Opis

It is known that Navier-Stokes equations is one of the most important equations in Fluid Mechanics and gas dynamics. On May 24, 2000, the Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named Navier-Stokes equations: Existence and smoothness of Navier-Stokes equations on $R^3$ as one of seven million problems. In this book, our aim is to study existence and asymptotic behavior of the Navier-Stokes equations and related models. The closely related models such as the Navier-Stokes-Poisson equations, Navier-Stokes-Korteweg equations,Jin-Xin model and Euler equations with damping are also studied. This book consists of three parts. Part 1 is to study the existence and zero dissipation limit of one-dimensional Navier-Stokes equations of compressible, isentropic and non-isentropic gases, and Jin-Xin model. The second part is about the existence and asymptotic behavior of the higher dimensional Navier-Stokes equations, Navier-Stokes-Poisson equations and Navier-Stokes-Korteweg equations. The third part is about the existence and asymptotic behavior of the isentropic and non-isentropic Euler equations with damping.

O autorze

Yinghui Zhang, PHD: Partial Differential Equations.Studied Mathematics at XiaMen University. Associate Professor at Hunan Institute of Science and Technology, Hunan, China.Zhong Tan, PHD: Partial Differential Equations.Studied Mathematics at Jilin University."Mingjiang" Special Professor at Xiamen University, Fujian, China.