Attractors for nonlinear autonomous dynamical systems / 非线性自治动力系统的吸引子 / 秦玉明, 苏克勤

This book introduces complete and systematic theories of infinite-dimensional dynamical systems and their applications in partial differential equations, especially in the models of fluid mechanics. It is based on the first author’s lecture “Infinite dimensional dynamical systems on nonlinear autonomous systems” given to graduate students in Donghua University since 2004. This book presents recent results that have been carried out by the authors on autonomous nonlinear evolutionary equations arising from physics, fluid mechanics and material science such as the Navier–Stokes equations, Navier–Stokes–Voight systems, the nonlinear thermoviscoelastic system, etc. 10.1051/978-2-7598-2703-9 (https://doi.org/10.1051/978-2-7598-2703-9) Contents Preface Chapter 1 Preliminary Chapter 2 Global Attractors for the Navier–Stokes–Voight Equations with Delay Chapter 3 Global Attractor and Its Upper Estimate on Fractal Dimension for the 2D Navier–Stokes–Voight Equations Chapter 4 Maximal Attractor for the Equations of One-Dimensional Compressible Polytropic Viscous Ideal Gas Chapter 5 UniversalAttractors for a NonlinearSystem of Compressible One-Dimensional Heat-Conducting Viscous Real Gas Chapter 6 Global Attractors for the Compressible Navier–Stokes Equations in Bounded Annular Domains Chapter 7 Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys Chapter 8 Global Attractors for Nonlinear Reaction–Diffusion Equations and the 2D Navier–Stokes Equations Chapter 9 Global Attractors for an Incompressible Fluid Equation and a Wave Equation References Index This book introduces complete and systematic theories of infinite-dimensional dynamical systems and their applications in partial differential equations, especially in the models of fluid mechanics. It is based on the first author's lecture “Infinite dimensional dynamical systems on nonlinear autonomous systems” given to graduate students in Donghua University since 2004. This book presents recent results that have been carried out by the authors on autonomous nonlinear evolutionar yequations arising from physics, fluid mechanics and material science such as the Navier–Stokes equations, Navier–Stokes–Voight systems, the nonlinear thermoviscoelastic system, etc.