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| Local Well-posedness of the Derivative Schr¨odinger Equation in Higher Dimension for Any Large Data |
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Citation： |
Boling GUO,Zhaohui HUO.Local Well-posedness of the Derivative Schr¨odinger Equation in Higher Dimension for Any Large Data[J].Chinese Annals of Mathematics B,2022,43(6):977~998 |
| Page view： 655
Net amount： 802 |
Authors： |
Boling GUO; Zhaohui HUO |
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| Abstract： |
In this paper, the authors consider the local well-posedness for the derivative Schr¨odinger equation in higher dimension ut ? i△u + |u|2(?→γ · ?u) + u2(?→λ · ?u) = 0, (x, t) ∈ Rn × R,?→γ ,?→λ ∈ Rn; n ≥ 2.It is shown that the Cauchy problem of the derivative Schr¨odinger equation in higher dimension is locally well-posed in Hs(Rn) (s > n/2) for any large initial data. Thus this result can compare with that in one dimension except for the endpoint space Hn/2. |
Keywords： |
Well-posedness, Derivative Schr¨odinger equation in higher dimension,Short-time Xs,b, Large initial data |
Classification： |
35E15, 35Q55 |
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