Abstract
Transonic flows past an obstacle such as an airfoil are first considered. A viscous approximation to the steady transonic flow problem is presented, and its convergence is obtained by the method of compensated compactness. Then the isometric embedding problem in geometry is discussed. A fluid dynamic formulation of the Gauss-Codazzi system for the isometric embedding of two-dimensional Riemannian manifolds is provided, and an existence result of isometric immersions with negative Gauss curvature is given.Key wordsTransonic flowviscosity methodEuler equationsgas dynamicscompensated compactnessentropy solutionsisometric embeddingtwo-dimensional Riemannian manifoldGauss-Codazzi systemnegative Gauss curvature
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