Find an appropriate concept of generalized solution, compatible with shock waves and other possible singularities, for which we can prove global existence and uniqueness of the initial value problem.
For generic data ?
5 Global, Singular, Solutions for the 3-D Systems of
Conservation Laws
MAIN OPEN PROBLEMS
NOTE OF CAUTION
A full treatment of the Compressible Euler equations must include the limiting case of the incompressible equations. This requires not only to settle the break-down conjecture 2 but also a way of continuing the solutions past singularities.
Need to work on vastly simplified model
problems.
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