Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 877 - 893, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017044

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Dung Le - Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, United States (email)

Abstract: 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.

Keywords:  Parabolic systems, Hölder regularity, $A_p$ classes, BMO weak solutions.
Mathematics Subject Classification:  Primary: 35J70, 35B65; Secondary: 42B37.

Received: September 2015;      Revised: December 2015;      Available Online: January 2017.