Abstract:

This paper studies the three-dimensional incompressible Euler flows in axisymmetric nozzles with a symmetric body. The well-posedness is established by stream function method and barrier function. Base on the above well-posedness, the far field convergence rates of the solutions are studied: if the infinite nozzles are the flat boundary outside the finite length, the solution of the equation converges to an asymptotic state at the exponential rate; if the infinite nozzles converge to the flat boundary with the polynomial rates, the solutions converge to the asymptotic states at the same polynomial rates.

Key words: Incompressible Euler equations, Axisymmetric Nozzles, Well-posedness, Convergence rates