2025/03/05 by Long, Bingsong
#35J25 #35J70 #35L65 #35L67 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.03406
In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under consideration is governed by the three-dimensional steady compressible Euler equations. Mathematically, this problem can be reformulated as an oblique derivative problem for a nonlinear degenerate elliptic equation in conical coordinates. By establishing a Lipschitz estimate, we show that the equation is uniformly elliptic in any subdomain strictly away from the degenerate boundary. Using this property, we further prove the existence of a solution to the problem via the continuity method and vanishing viscosity method.