Global Problems, Global Solutions: Prospects for a Better World approaches social problems from a global perspective with an emphasis on using one’s sociological imagination. Perfect for instructors who involve students in research, this text connects problems borne by individuals to regional, global and historical forces, and stresses the importance of evidence in forming opinions and policies addressing social issues. The book introduces readers to the complexities of the major problems that confront us today such as violent conflict, poverty, climate change, human trafficking and other issues that we encounter in our lives. It book concludes with a chapter on politics and government, underscoring the need for good governance at all levels–and cooperation among many layers of government–to build a better world.

The book is based on global economic and social crisis today and in the future, and how to solve some of this global chaos and crisis.

The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.

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References: p.403-415.

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