The aim of this paper is to study the global unique solvability on Sobolev solution perturbated around diffusion waves to the Cauchy problem of conservative form of Hsieh's equations. Furthermore, convergence rates are also obtained as one of the diffusion parameters goes to zero. The difficulty is created due to conservative nonlinearity to enclose the uniform (in diffusion parameter) higher order energy estimates. However this kind of difficulty will not occur for both the nonconservative nonlinearity and fixed diffusion parameter. The more subtle mathematical analysis needs to be introduced to overcome the difficulties.

中文翻译：

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Hsieh方程的守恒形式对消失扩散极限的收敛速度

本文的目的是研究围绕扩散波扰动的Sobolev解对Hsieh方程的保守形式的Cauchy问题的全局唯一可解性。此外，当扩散参数之一变为零时，也获得收敛速度。由于保守的非线性来封闭均匀的（在扩散参数中）高阶能量估计而造成了困难。但是，对于非保守非线性和固定扩散参数都不会发生这种困难。需要引入更细微的数学分析来克服这些困难。