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Volume 2,     Number 3,     Summer 1994

 

SMOOTH GLOBAL SOLUTIONS OF THE
TWO DIMENSIONAL BURGERS EQUATION
KAZUO ITO

Abstract. It is shown in the present paper that the two dimensional Burgers equation describing a quasi-plane wave in a viscous heat conducting fluid admits smooth global solutions, provided initial data are smooth and small. Solutions decay at infinite time in a prescribed single space direction like those of the one-dimensional linear heat equation.

 

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