# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 37 (2008) pp.463-492

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### Abstract

In this paper we prove two results on the Levi conditions for weakly hyperbolic systems with characteristics of constant multiplicities. A first result concerns scalar operators: we prove that Levi conditions defined by the second author in [29] are equivalent to the usual Levi conditions for scalar operator. A second result concerns systems whose principal symbol has a Jordan form made of a large number of 2 \times 2 blocks. For these systems we express the first Levi condition via an invariant constructed from the sub-characteristic matrix. Moreover we show that this condition is necessary for the C^\infty well-posedness.

MSC(Primary) 35L45 Cauchy problem for systems with constant multiplicities, Levi conditions.