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New global a prior; estimates for the third-grade fluid equations
Steinhauer, Mark; Urbano, José Miguel; Videman, JuhaThis note bridges the gap between the existence and regularity classes for the third-grade Rivlin-Ericksen fluid equations. We obtain a new global a priori estimate, which conveys the precise regularity conditions that lead to the existence of a global in time regular solution. Copyright © 2006 John Wiley & Sons, Ltd. ; http://dx.doi.org/10.1002/mma.732
New global a priori estimates for the third-grade fluid equations
Steinhauer, Mark; Urbano, José Miguel; Videman, JuhaThis note bridges the gap between the existence and regularity classes for the solutions of the third-grade Rivlin-Ericksen fluid equations. We obtain a new global a priori estimate which conveys the precise regularity conditions that lead to the existence of a global in time regular solution
Unidirectional steady flow of a viscoelastic fluid with a free surface
Urbano, José Miguel; Videman, Juha H.We study the steady flow of a second grade fluid down an open inclined channel. We formulate the mathematical problem, a mixed boundary value problem for the Laplacian with an unknown free boundary described by a nonlinear second order ODE, and prove existence of a unique solution for small data using a contraction argument.
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