论文标题
强/经典解决方案的全球存在和消失的分散限制对具有大初始数据的一维压缩量子Navier-Stokes方程
Global Existence and Vanishing Dispersion Limit of Strong/Classical Solutions to the One-dimensional Compressible Quantum Navier-Stokes Equations with Large Initial Data
论文作者
论文摘要
我们关注的是，强/经典解决方案的全球存在和消失的分散限制对一维强度可压缩量子量子 - 纳维尔 - 长方形方程式的库奇问题，该方程由可压缩的navier-stokes方程组成，由线性密度依赖性粘度和非线性三级差异型运算量与量子量相关。 $ p（ρ）=ρ^γ$被认为是一个常数的情况。当粘度常数$ν$和普朗克常数$ \ varepsilon $不相等时，我们将重点放在情况下。在一些关于$ν，\ varepsilon，γ$和初始数据的合适假设下，我们证明了从真空到可压缩的量子纳维尔 - 孔 - 斯托克斯方程的全球存在和大型经典溶液的大量行为，并具有任意大的初始数据。该结果将可压缩量子Navier-Stokes方程的全球强大振幅解决方案的构建扩展到了$ν\ neq \ varepsilon $。此外，还以某些收敛速率确定了量子Navier-Stokes方程的经典解决方案的消失分散极限。该证明是基于新的有效速度，该速度将量子Navier-Stokes方程转换为抛物线系统，并进行了一些详尽的估计，以得出特定体积上均匀的时间正上下和上限。
We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional barotropic compressible quantum Navier-Stokes equations, which consists of the compressible Navier-Stokes equations with a linearly density-dependent viscosity and a nonlinear third-order differential operator known as the quantum Bohm potential. The pressure $p(ρ)=ρ^γ$ is considered with $γ\geq1$ being a constant. We focus on the case when the viscosity constant $ν$ and the Planck constant $\varepsilon$ are not equal. Under some suitable assumptions on $ν,\varepsilon, γ$, and the initial data, we proved the global existence and large-time behavior of strong and classical solutions away from vacuum to the compressible quantum Navier-Stokes equations with arbitrarily large initial data. This result extends the previous ones on the construction of global strong large-amplitude solutions of the compressible quantum Navier-Stokes equations to the case $ν\neq\varepsilon$. Moreover, the vanishing dispersion limit for the classical solutions of the quantum Navier-Stokes equations is also established with certain convergence rates. The proof is based on a new effective velocity which converts the quantum Navier-Stokes equations into a parabolic system, and some elaborate estimates to derive the uniform-in-time positive lower and upper bounds on the specific volume.
