论文标题
时间呈现的膨胀，剩余的剩余估计值1D粘性流量
Time-asymptotic expansion with pointwise remainder estimates for 1D viscous compressible flow
论文作者
论文摘要
我们构建了一个时间 - 肿瘤扩展，对1D可压缩Navier的解决方案的剩余估计值 - 稳定方程。前阶项是众所周知的扩散波，高阶项是新引入的波浪家族，我们称之为\ textit {高阶扩散波}。特别是，这些提供了围绕原点$ x = 0 $的解决方案的幂律渐进性的准确描述，而扩散波呈指数衰减。该扩展在本地和全球范围内在$ l^p（\ mathbb {r}）$中 - norm-norm for All $ 1 \ leq p \ leq \ leq \ infty $。该证明基于对格林功能的重点估计。
We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced family of waves which we call \textit{higher-order diffusion waves}. In particular, these provide accurate description of the power-law asymptotics of the solution around the origin $x=0$ where the diffusion wave decays exponentially. The expansion is valid locally and also globally in the $L^p(\mathbb{R})$-norm for all $1\leq p\leq \infty$. The proof is based on pointwise estimates of Green's function.
