论文标题
Strichartz对结构化Lipschitz系数方程的估计值
Strichartz estimates for equations with structured Lipschitz coefficients
论文作者
论文摘要
证明了Schrödinger和Lipschitz系数满足其他结构假设的Schrödinger和波动方程的尖锐估计。我们使用Phillips功能演算作为傅立叶反转的替代品，它显示了如何从恒定系数的情况下继承分散性能。遵循的全球Strichartz估计值规定，系数的衍生物是可集成的。估计值扩展到有界变化的结构化系数。作为应用，我们得出了Strichartz的估计值，并具有带有Hölder连续系数的波方程的额外导数损失，并求解了非线性Schrödinger方程。最后，我们记录了频谱乘数估计值，这是从众所周知的均值估计中得出的。
Sharp Strichartz estimates are proved for Schrödinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how dispersive properties are inherited from the constant coefficient case. Global Strichartz estimates follow provided that the derivatives of the coefficients are integrable. The estimates extend to structured coefficients of bounded variations. As applications we derive Strichartz estimates with additional derivative loss for wave equations with Hölder-continuous coefficients and solve nonlinear Schrödinger equations. Finally, we record spectral multiplier estimates, which follow from the Strichartz estimates by well-known means.
