Nonexistence Of A Global Nontrivial Subsonic Solution Past An Unbounded 3D Ramp

In this paper, we study the nonexistence of a global nontrivial subsonic solution in an unbounded 3D ramp Q. 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 prior estimate on the solution of Laplace equation in Q with Neumann boundary condition on ?Q. At the same time, it can overcome the difficulty of the singularity and the infinite distance on2 x. we proved that there is no global nontrivial subsonic flow with low Mach number in such domain. This paper extended the result in [17] to a full 3D ramp case. In the proof of Lemma 3.1 and Lemma 3.4, the existence and uniqueness of the solution of the equation, due to the lack of infinity and edge information, we cannot use maximum principle, this paper uses the separation of variables and modified Bessel function to prove.