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GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS
Preview AbstractThe authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.
GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY
Preview AbstractConsider the following Cauchy problem for the first order quasilinear strictly hyperbolic system
We let
The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u=u(t,x) for all t∈R, provided that
