We consider the Cauhcy problem to the 3D diffusive periodic Burgers equation. We prove that a unique solution exists on time interval independent of the viscosity and tends, as the viscosity vanishes, to the solution of the limiting equation, the inviscid periodic three-dimensional Burgers equation, in Gevrey–Sobolev spaces. Compared to Navier–Stokes equations, the main difficulties come from the lack of the divergence-free condition which is essential to handle the nonlinear term. Our alternative tool will be to use a change of functions to estimate nonlinearities. Fourier analysis and compactness methods are widely used.

中文翻译：

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Gevrey类中3D Burgers方程的粘度极限逐渐消失

我们将Cauhcy问题考虑到3D扩散周期性Burgers方程。我们证明了在不依赖粘度的时间间隔上存在唯一解，并且随着粘度的消失，趋向于在Gevrey–Sobolev空间中的极限方程，无粘性周期三维Burgers方程的解。与Navier–Stokes方程相比，主要困难来自缺乏无散度条件，这对于处理非线性项至关重要。我们的替代工具将使用函数的变化来估计非线性。傅里叶分析和紧实度方法被广泛使用。