Document View

First, we apply the compensated compactness framework to proving the existence of global entropy solutions in L ^∞ to the multidimensional Euler equations and Euler-Poisson equations for compressible isothermal gas dynamics with spherically symmetric initial data that allows vacuum and unbounded velocity outside a solid ball.

In the second part, we establish a compactness framework for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing a new approach to employ these new properties into the method of compensated compactness. Then this framework is applied to establishing the existence, compactness, and decay of entropy solutions in L ^∞ for the Euler equations in nonlinear elastodynamics.