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On the inviscid limit of the diffusive 3D periodic Burgers equations in Sobolev spaces

Abir Sboui, Ridha Selmi

Abstract



We prove local in time well-posedness of solution to the viscous and non-viscous three dimensional periodic Burgers equations. We establish convergence of the viscous solution to the non-viscous one and give its rate, as the viscosity vanishes. Such convergence is uniform in time with respect to viscosity. Moreover, we present some ideas that may help interested researchers to ameliorate this convergence result. We use energy methods in large indexes Sobolev spaces.

Keywords


Burgers equations, viscous and non-viscous solution, existence and uniqueness, vanishing viscosity, convergence and rate of convergence.

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