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    STUDIA MATHEMATICA - Issue no. 4 / 2007  
         
  Article:   BOOK REVIEWS - MATHEMATICAL ASPECTS OF NONLINEAR DISPERSIVE EQUATIONS, JEAN BOURGAIN,CARLOS E. KENIG & S. KLAINERMAN (EDITORS), ANNALS OF MATHEMATICS STUDIES NO. 163,PRINCETON UNIVERSITY PRESS, PRINCETON AND OXFORD 2007, VII + 300 PP..

Authors:  RADU PRECUP. 		 
       
         
  Abstract:  These are the written versions of a number of lectures delivered at the CMI/IAS Workshop on mathematical aspects of nonlinear PDEs, in the spring of 2004 at the Institute for Advanced Study in Princeton. The workshop is a conclusion of a year-long program at IAS about this topic, leading to significant progress and to the broadening of the subject. At least two important breakthroughs were obtained - the first one is the understanding of the blowup mechanism for critical focusing Schr¨odinger equation, and the other is a proof of global existence and scattering for the 3D quintic equation for general smooth data. In both cases, hard analysis, in addition to the more geometric approach, turned to play a key role in energy estimates.  
         
     
         
         
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