| Abstract: |
| We develop a new bilinear estimate method based on a new div curl lemma. We can use our method to give alternative proof of low regularity local well posedness for dispersive equations, which previously rely on Bourgain space. We can also use our method to give new proof of global existence of classical solutions for nonlinear wave equations with small initial data. Moreover, we establish new results including the proof of Weiyue Ding`s conjecture for periodic Schrodinger flow, the global well posedness in the critical Besov space of the skew mean curvature flow and the gloabl well posednee in critical Sobolev space of Ishimori equations. |
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