MAIN OPEN PROBLEMS
Known Results
For any smooth initial data there exists
a T>0 and a unique solution in [0,T]_R3.
There exist arbitrarily small perturbations of the trivial data set
which break-down in finite time
Local in time existance
Singularities
(JOHN, SIDERIS)
1-D Global Existence
and Uniqueness
(GLIMM, BRESSAN-LIU-YANG)
Global existence and uniqueness for
all initial data with small bounded variation.
5 Global, Singular, Solutions for the 3-D Systems of
Conservation Laws
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