Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type
We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.
Two-dimensional Navier-Stokes flow in unbounded domains.
Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries.
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