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Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions. (English) Zbl 1263.35127

Summary: We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.

MSC:

35K35 Initial-boundary value problems for higher-order parabolic equations
35B65 Smoothness and regularity of solutions to PDEs
35K55 Nonlinear parabolic equations
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