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Abstract: |
Nonunique, and pathological, solutions of the Euler equation have been constructed. They serve a useful role as counterexamples to any existence theory. In this mode, they defy most proposed admissibility conditions. We formulate a fundamental admissibility condition, based on laws of physics. The admissible solution should have a maximum rate of entropy dissipation relative to all possible solutions of the Euler equation with common initial conditions. We believe that the obviously pathological solutions are thereby excluded. We present physics arguments (numerical tests to follow) that commonly used ILES simulation models fail this criteria. The status of alternate simulations, based on dynamic subgrid scale terms and Front Tracking will be reviewed.
Prof. James Glimm，纽约州立大学石溪分校，美国科学院院士，前美国数学会会长。国际著名数学家，曾获美国总统奖。 |