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Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

✍ Scribed by M Nakamura; T Ozawa

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
310 KB
Volume
155
Category
Article
ISSN
0022-1236

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✦ Synopsis

The Cauchy problem for the nonlinear Schro dinger equations is considered in the Sobolev space H nÂ2 (R n ) of critical order nÂ2, where the embedding into L (R n ) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for global H nÂ2 -solutions with small Cauchy data.

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