论文标题
半连续二阶进化方程的库奇问题，带有分数拉普拉斯和阻尼
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
论文作者
论文摘要
在本文中，我们证明了加权Sobolev空间中解决方案的时间衰减估计值，以二阶进化方程，分数laplacian和在BESOV空间中的数据进行阻尼。我们的估计概括了先前研究中获得的估计值。本文的第二个目的是应用这些估计值，以证明与功率非线性方程问题的库奇问题有关的小数据全球辅助性。尤其是，本文获得的估计值使我们能够比以前的研究结果对待非线性和空间维度的更一般条件。
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates obtained in the previous studies. The second aim of this article is to apply these estimates to prove small data global well-posedness for the Cauchy problem of the equation with power nonlinearities. Especially, the estimates obtained in this paper enable us to treat more general conditions on the nonlinearities and the spatial dimension than the results in the previous studies.
