论文标题
局部良好的不稳定电势流的稳定性，在直角的空间角附近
Local Well-posedness of Unsteady Potential Flows Near a Space Corner of Right Angle
论文作者
论文摘要
在本文中，我们关注的是，在直角的空间角附近的不稳定电势流的局部良好性，这可以作为在拐角处空间域中二阶的双曲线方程的初始有限值问题进行配合。角落的奇异性是建立问题的当地良好性的关键困难。此外，角角两个边缘的边界条件都是诺伊曼类型的，无法满足线性稳定性条件，这使得在分析中对边界项建立先验估计更加困难。在本文中，将更新扩展方法来处理角落的奇点，并且基于关键观察，即边界运营商是共同正常的，将开发新技术来控制边界项。
In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a cornered-space domain. The corner singularity is the key difficulty in establishing the local well-posedness of the problem. Moreover, the boundary conditions on both edges of the corner angle are of Neumann-type and fail to satisfy the linear stability condition, which makes it more difficult to establish a priori estimates on the boundary terms in the analysis. In this paper, extension methods will be updated to deal with the corner singularity, and, based on a key observation that the boundary operators are co-normal, new techniques will be developed to control the boundary terms.
