Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\"odinger equation
Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\"odinger equation
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DOI：
10.14492/hokmj/1249046372
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发表时间：
2007-08
期刊：
影响因子：
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通讯作者：
Y. Tsutsumi
中科院分区：
文献类型：
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作者：
Y. Tsutsumi
我们研究了非线性薛定谔方程柯西问题解的无条件唯一性。我们在空间维度和非线性幂的某些假设下，展示了临界情况下 C([0, T]; H s ) 或亚临界情况下 L°°(0, T; H s ) 中解的唯一性。我们不假设解属于与 Strichartz 估计相关的任何辅助空间。为此，我们还证明了函数和分布之间的乘积估计以及映射的连续性：u →|u|在齐次 Sobolev 或 Besove 空间上。
We study the unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schrodinger equation. We show the uniqueness of solution in C([0, T]; H s ) for the critical case or L°°(0, T; H s ) for the subcritical case under certain assumptions on spatial dimensions and power of nonlinearity. We do not assume the solution belongs to any auxiliary spaces associated with the Strichartz estimate. For that purpose, we also prove the estimate of product between functions and distributions and the continuity of mapping: u →|u| on the homogeneous Sobolev or Besove space.