Related papers: The Cauchy problem for Schrodinger flows into Kahl…

The paper has been withdrawn because of a more complete analysis of the relativistic fluid including the quantization reported in arxiv:0801.3032 [hep-th].

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This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.

This paper has been withdrawn by the author due to some problems. Please contact me.

In this paper, we develop a novel idea to study $y$-dependence for the logarithmic Schr\"odinger equation on $\mathbb{R}^d \times \mathbb{T}^n$. Unlike \cite{STNT2014}(Analysis \& PDE, 2014) and \cite{HHYL2024}(SIAM J. Math. Anal., 2024),…

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This paper was withdrawn by the author due to an edition's rights

This paper has been withdrawn by the author due to serious error found in main argument.

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This paper has been withdrawn by the authors until some changes are made.

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This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.

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In this paper, the author has considered the hyperbolic Kahler-Ricci flow introduced by Kong and Liu [11], that is, the hyperbolic version of the famous Kahler-Ricci flow. The author has explained the derivation of the equation and…

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In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the…

This paper has been withdrawn by the authors due to an unlikely results.

This paper has been withdrawn by the author.