论文标题
辐射场和对能亚临界波方程的非辐射溶液
Radiation fields and non-radiative solutions to the energy sub-critical wave equations
论文作者
论文摘要
近年来，辐射场和能量方法的通道已成为研究非线性波方程的重要工具。在这项工作中，我们在能量亚临界情况下给出了自由波的辐射场的基本理论。我们还表明，针对多种非线性波方程的非辐射溶液的渐近行为类似于非辐射自由波的行为。我们的理论完全在相应的非线性波方程的临界Sobolev空间中给出，并避免了对溶液能量的任何假设。
Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fields of free waves in the energy sub-critical case. We also show that the asymptotic behaviours of non-radiative solutions to a wide range of non-linear wave equations resemble those of non-radiative free waves. Our theory is completely given in the critical Sobolev spaces of the corresponding nonlinear wave equation and avoids any assumption on the energy of the solutions.
