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An attached oblique shock wave is generated when a sharp solid projectile flies supersonically in the air. We study the linear stability of oblique shock waves in steady supersonic flow under three dimensional perturbation in the incoming flow. Euler system of equations for isentropic gas model is used. The linear stability is established for shock front with supersonic downstream flow, in addition to the usual entropy condition.

We study the conic shock waves for 3-dimensional steady irrotational isentropic supersonic flow against a sharp symmetrically curved conic projectile. An approximate solution was constructed and the existence of a conic shock wave solution is established by linear iteration.

We study the structure of Riemann solutions for 2-dimensional scalar conservation laws. The Riemann data are three constants in three fan domains forming different angles. We study the dependence of the structure of the solution upon the value of the constants as well as the angles.