Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up of solutions, conservation laws, Hamiltonian systems, and others.The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. The event allowed the international mathematics community to honor two of its outstanding members.
Scaling laws and vanishing viscosity limits in turbulence theory by G. I. Barenblatt and A. J. Chorin Potential theory in Hilbert spaces by P. Cannarsa and G. Da Prato Recent developments in the theory of the Boltzmann equation by C. Cercignani New results for the asymptotics of orthogonal polynomials and related problems via the Lax-Levermore method by P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin Evolution of trajectory correlations in steady random flows by A. Fannjiang, L. Ryzhik, and G. Papanicolaou Integrability: From d'Alembert to Lax by A. S. Fokas Methods in the theory of quasi periodic motions by G. Gallavotti Fourier analysis and nonlinear wave equations by S. Klainerman The KdV zero-dispersion limit and densities of Dirichlet spectra by C. D. Levermore On Boltzmann equation and its applications by P.-L. Lions Simplified asymptotic equations for slender vortex filaments by A. J. Majda Homoclinic orbits for pde's by D. W. McLaughlin and J. Shatah Lagrangian metrics on fractals by U. Mosco Approximate solutions of nonlinear conservation laws and related equations by E. Tadmor The small dispersion KdV equation with decaying initial data by S. Venakides.