Abstract:
The Riemann problem for the equations of pressureless fluid dynamics was considered. Solutions of this problem were constructed by employing the viscosity vanishing approach. For some initial data, solutions showed high singularity around the shock waves. A new mathematical theory of generalized functions initiated by J.F. Colombeau was applied to dealing with the multiplication of singular distributions. As a byproduct, the entropy condition was obtained for singular distribution solutions.
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Received: 2 May 1997 / Accepted: 6 October 1997
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Hu, J. The Riemann Problem for Pressureless Fluid Dynamics with Distribution Solutions in Colombeau's Sense . Comm Math Phys 194, 191–205 (1998). https://doi.org/10.1007/s002200050355
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DOI: https://doi.org/10.1007/s002200050355