On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases
On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases
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DOI：
10.1016/j.matpur.2019.10.003
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
K. Fujiwara;V. Georgiev;T. Ozawa
中科院分区：
文献类型：
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作者：
K. Fujiwara;V. Georgiev;T. Ozawa
本文研究了欧氏空间上具有幂类型非线性的半相对论方程的整体适定性。在具有1≤S≤2的二维H-S标度次临界情形下，由Strichartz估计得到了系统的局部适定性。在高维H1标度次临界情形下，径向解的局部适定性由加权的Strichartz估计得到。此外，在三维H1尺度临界情况下，径向解的局部适定性是由相应的一维问题得到的解的一致界得到的。局部解可以通过先验估计来扩展。
In this paper, the global well-posedness of semirelativistic equations with a power type nonlinearity on Euclidean spaces is studied. In two dimensional H s scaling subcritical case with 1≤ s≤ 2, the local well-posedness follows from a Strichartz estimate. In higher dimensional H 1 scaling subcritical case, the local well-posedness for radial solutions follows from a weighted Strichartz estimate. Moreover, in three dimensional H 1 scaling critical case, the local well-posedness for radial solutions follows from a uniform bound of solutions which may be derived by the corresponding one dimensional problem. Local solutions may be extended by a priori estimates.