Global existence of the two-dimensional axisymmetric Euler equations for the Chaplygin gas with large angular velocities

Abstract

The Chaplygin gas model is both interesting and important in the theory of gas dynamics and conservation laws, all the characteristic families of which are linearly degenerate. Majda conjectured that the shock formation never happens for smooth data. In this article, we prove the conjecture for the two space dimensional axisymmetric case. Different from previous approaches to study wave equations with different speeds, we reformulate the problem in the Lagrangian coordinates and consider a single wave equation with variable coefficients. This not only gives a simpler proof but also enables us to treat the case with large angular velocities.

Keywords

• chaplygin gas
• global existence
• wave equation
• variable coefficients
• 35b07
• 35l05
• 35q31
• 76n10