论文标题
非等级冲击形成的粘性汉堡的无粘性极限
The inviscid limit of viscous Burgers at nondegenerate shock formation
论文作者
论文摘要
我们研究了非排定冲击形成附近的一维汉堡方程的消失粘度极限。我们开发了匹配的渐近扩张，该扩展描述了小型粘度解决方案，直到第一次冲击形成那一刻。该扩展的内部具有基于Inviscid溶液的分数时空泰勒序列的新结构。我们在各种规范中获得了急剧消失的粘度率，包括$ l^\ infty $。可比较的先前结果分解在冲击形成附近。我们部分填补了这个空白。
We study the vanishing viscosity limit of the one-dimensional Burgers equation near nondegenerate shock formation. We develop a matched asymptotic expansion that describes small-viscosity solutions to arbitrary order up to the moment the first shock forms. The inner part of this expansion has a novel structure based on a fractional spacetime Taylor series for the inviscid solution. We obtain sharp vanishing viscosity rates in a variety of norms, including $L^\infty$. Comparable prior results break down in the vicinity of shock formation. We partially fill this gap.
