{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/126921"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/126921","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The role of smoothing effect in some dispersive equations","abstract":"In this thesis, we study the role of smoothing effect in the local well-posedness theory of dispersive partial differential equations in three different contexts. First, we use it to overcome a loss of derivatives in a family of nonlocal dispersive equations. Second, we exploit a discrete version of the smoothing effect to study a discrete system of particles and how to approximate it by a continuous dispersive equation. 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