本书介绍了非线性偏微分方程现代理论及其应用的某些领域中的最新研究进展。这些领域中的指引者在邀请演讲中提出的主题包括如下内容：湍流、稀薄气体的动力学模型、涡丝、色散波、奇异极限和解的破裂（膨胀变换）、守恒定律、哈密尔顿系统等内容。本书的目的是记录这些演讲内容：希尔伯特空间中的势论、平稳随机流中轨迹相关性的演化、准周期运动理论中的方法、傅里叶分析与非线性波方程等内容。本书适合数学物理学专业的师生及爱好者参考阅读。

Preface
List of funding institutions and other sponsors
Scaling laws and vanishing viscosity limits in turbulence theory
G. I. BARENBLATT AND ALEXANDRE J. CHORIN
Potential theory in Hilbert spaces
PIERMARCO CANNARSA AND GIUSEPPE DA PRATO
Recent developments in the theory of the Boltzmann equation
CARLO CERCIGNANI
New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method
P. DEIFT, T. KRIECHERBAUER, AND K. T-R MCLAUGHLIN
Evolution of trajectory correlations in steady random flows
ALBERT FANNJIANG, LEONID RYZHIK, AND GEORGE PAPANICOLAOU
Integrability: from d'Alembert to Lax
A. S. FOKAS
Methods in the theory of quasi periodic motions
GIOVANNI GALLAVOTTI
Fourier analysis and nonlinear wave equations
SERGIU KLAINERMAN
The KdV zero-dispersion limit and densities of Dirichlet spectra
C. DAVID LEVERMORE
On Boltzmann equation and its applications
PIERRE-LOUIS LIONS
Simplified asymptotic equations for slender vortex filaments
ANDREW J. MAJDA
Homoclinic orbits for pde's
DAVID W. MCLAUGHLIN AND JALAL SHATAH
Lagrangian metrics on fractals
UMBERTO MOSCO
Approximate solutions of nonlinear conservation laws and related equations
ETTAN TADMOR
The small dispersion KdV equation with decaying initial data
S. VENAKIDES
编辑手记