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The phenomenon of steady streaming, or acoustic streaming, is an importantphysical phenomenon studied extensively in the literature. Its mathematicalformulation involves the Navier-Stokes equations, thus due to the complexity ofthese equations is usually studied heuristically using formal perturbationexpansions. It turns out that the Burgers equation formulated on the half lineprovides a simple model of the above phenomenon. The physical situationcorresponds to the solution of the Dirichlet problem on the half-line, whichdecays as $x \to \infty$ and which is {\it time periodic}. We show that theDirichlet problem, where the usual prescription of the initial condition is nowreplaced by the requirement of the time periodicity, yields a well posedproblem. Furthermore, we show that the solution of this problem tends to the``inner'' and ``outer'' solutions obtained by the perturbation expansions

The Time Periodic Solution of the Burgers Equation on the Half-Line and an Application to Steady Streaming