On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
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DOI：
10.2969/jmsj/06920459
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发表时间：
2014-04
期刊：
影响因子：
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通讯作者：
Jonathan Bennett;N. Bez;Chris Jeavons;N. Pattakos
中科院分区：
文献类型：
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作者：
Jonathan Bennett;N. Bez;Chris Jeavons;N. Pattakos
我们对自由薛定谔方程解u的Ozawa-Tsutsumi型尖锐双线性估计进行了全面的分析，它给出了对$的尖锐控制。|u| ^2 $在经典Sobolev空间中。特别是，我们提供了一个推广他们的估计，以这样一种方式，提供了一个统一的一些尖锐的双线性估计证明了Escheriro和Planchon-Vega，通过完全不同的方法，看到他们所有的特殊情况下，一个参数家庭的尖锐估计。我们证明了极值函数是Maxwell-Boltzmann泛函方程的解，并提供了一个新的证明，该方程只允许高斯解。我们还联系到某些涉及某些色散Sobolev范数的关于u^2 $的尖锐估计。
We provide a comprehensive analysis of sharp bilinear estimates of Ozawa-Tsutsumi type for solutions u of the free Schrodinger equation, which give sharp control on $|u|^2$ in classical Sobolev spaces. In particular, we provide a generalization of their estimates in such a way that provides a unification with some sharp bilinear estimates proved by Carneiro and Planchon-Vega, via entirely different methods, by seeing them all as special cases of a one parameter family of sharp estimates. We show that the extremal functions are solutions of the Maxwell-Boltzmann functional equation and provide a new proof that this equation admits only Gaussian solutions. We also make a connection to certain sharp estimates on $u^2$ involving certain dispersive Sobolev norms.