The purpose of the present article is to study weak solutions of viscous conservation laws in physics. We are interested in the well-posedness theory and the propagation of singularity in the weak solutions for the initial value problem. Our approach is to convert the differential equations into integral equations on the level of weak solutions. This depends on exact analysis of the associated linear equations and their Green's functions. We carry out our approach for the Navier-Stokes equations in gas dynamics. Local in time as well as time-asymptotic behaviors of weak solutions, and the continuous dependence of the solutions on their initial data are established. © 2022 Wiley Periodicals LLC.

中文翻译：

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气体动力学中的 Navier-Stokes 方程：格林函数、奇异性和适中性

本文的目的是研究物理学中粘性守恒定律的弱解。我们对适定性理论和奇点在初值问题的弱解中的传播感兴趣。我们的方法是在弱解水平上将微分方程转化为积分方程。这取决于对相关线性方程及其格林函数的精确分析。我们对气体动力学中的 Navier-Stokes 方程进行了研究。建立了弱解的时间局部性和时间渐近行为，以及解对其初始数据的连续依赖性。© 2022 威利期刊有限责任公司。