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On the singularities of solutions to 4-D semilinear dispersive wave equations |
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| Authors: | Ning Xu Huicheng Yin |
| Affiliation: | (1) Department of Mathematics and MIS, Nanjing University, 210093 Nanjing, P. R. China;(2) Department of Basic Course, PLA Nanjing Institute of Politics, 210003 Nanjing, P. R. China |
| Abstract: | In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point. Combining Strichartz's inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal. |
| Keywords: | Dispersive wave equation tangent vector fields Strichartz's inequality pseudodiffer ential operator WAVE EQUATIONS SEMILINEAR SOLUTIONS show Cauchy initial data inequality commutator techniques global singularity structures weak solutions semilinear wave equations single point note |
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