On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrodinger Equation
On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrodinger Equation
复制标题
Loglog能量-超临界薛定谔方程非光滑径向散射解的Jensen型不等式
DOI：
10.1093/imrn/rny045
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发表时间：
2018
影响因子：
1
通讯作者：
Tristan Roy
中科院分区：
文献类型：
--
作者：
Setsuro Fujiie;Andre Martinez and Takuya Watanabe;Takafumi Amaba;菅徹;Tristan Roy
我们证明了对数能量-超临界Schrödinger方程解的散射性，其中n∈{3,4,5}，径向数据，其中n∈{3,4}。n = 5)。证明使用集中技术（参见例如，[,]）来证明在任意长的时间间隔上的长期Strichartz-type估计，这取决于解决方案的一些规范的优先界，结合对Strichartz估计的时间的归纳，以便对这些规范进行后验约束（参见例如，[,]）。我们还重新讨论了具有径向数据的解的散射理论，，和n∈{3,4}；更准确地说，我们证明了在更大范围内的散射。为了控制非光滑解（即数据为的解）的勉强超临界非线性，我们证明了一些jensen型不等式。
We prove scattering of solutions of the loglog energy-supercritical Schrödinger equationwith,,n∈ {3, 4, 5}, and with radial data, whereifn∈ {3, 4} (resp.n= 5). The proof uses concentration techniques (see e.g., [ , ]) to prove a long-time Strichartz-type estimate on an arbitrarily long time intervalJdepending on ana prioribound of some norms of the solution, combined with an induction on time of the Strichartz estimates in order to bound these normsa posteriori(see e.g., [ , ]). We also revisit the scattering theory of solutions with radial data in,, andn∈ {3, 4}; more precisely, we prove scattering for a larger range ofs than in . In order to control the barely supercritical nonlinearity for nonsmooth solutions, that is, solutions with data in,, we prove some Jensen-type inequalities.