Abstract
The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the L∞-initial data in the class of weak entropy solutions. As a consequence, there are infinitely many measure-valued solutions for a vast set of initial data. Finally, using the concept of relative energy, we discuss a singular limit problem for the measure-valued solutions, where the Mach and Froude number are proportional to a small parameter.
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