Abstract
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.