TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

doi:10.1007/s10473-022-0416-1

Abstract

Abstract: In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation, which tends to a given radially symmetric subsonic spiral flow at far field. The optimal decay rate at far field is also derived by Kelvin’s transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compensated compactness framework.

Key words: Subsonic spiral flows, Euler equations, subsonic-sonic limit, a porous body

CLC Number:

35B40

Shangkun WENG, Zihao ZHANG. TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY[J].Acta mathematica scientia,Series B, 2022, 42(4): 1569-1584.

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