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Global existence and regularity results for strongly coupled nonregular parabolic systems via iterative methods

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Dedicated to Professor Stephen Cantrell on the occasion of his 60th birthday

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  • The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's results on global existence of classical solutions still hold under much weaker condition that their BMO norms do not blow up in finite time. The proof makes use of some new global and local weighted Gagliardo-Nirenberg inequalities involving BMO norms.

    Mathematics Subject Classification: Primary:35J70, 35B65;Secondary:42B37.


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