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On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain

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Abstract

In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on ∂Ω and Dirichlet boundary value at some point of ∂Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.

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Authors and Affiliations

  1. Department of Mathematics & IMS, Nanjing University, Nanjing, 210093, China

    Jun Li, HuiCheng Yin & ChunHui Zhou

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  1. Jun Li
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  2. HuiCheng Yin
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  3. ChunHui Zhou
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Correspondence to HuiCheng Yin.

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Li, J., Yin, H. & Zhou, C. On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain. Sci. China Math. 53, 1753–1766 (2010). https://doi.org/10.1007/s11425-010-4028-1

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  • DOI: https://doi.org/10.1007/s11425-010-4028-1

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