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Global well-posedness of Korteweg–de Vries equation in

✍ Scribed by Zihua Guo

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
215 KB
Volume
91
Category
Article
ISSN
0021-7824

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✦ Synopsis

We prove that the Korteweg-de Vries initial-value problem is globally well-posed in H -3/4 (R) and the modified Kortewegde Vries initial-value problem is globally well-posed in H 1/4 (R). The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation in H -3/4 by constructing some special resolution spaces in order to avoid some 'logarithmic divergence' from the high-high interactions. Our local solution has almost the same properties as those for H s (s > -3/4) solution which enable us to apply the I-method to extend it to a global solution.

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