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摘要
The Neumann boundary value problem for the chemotaxis system generalizing the prototype {u(t) = del . (D(u)del u) - del . (u del v), x is an element of Omega, t > 0, (KS) v(t) = Delta(v) - uv, x is an element of Omega, t > 0, is considered in a smooth bounded convex domain Omega subset of R-N (N >= 2), where D(u) >= CD (u + 1) m(-1) for all u >= 0 with some m > 1 and C-D > 0. If m > 3N/2+N2 and suitable regularity assumptions on the initial data are given, the corresponding initial-boundary problem possesses a global classical solution. Our paper extends the results of Wang et al. ([21]), who showed the global existence of solutions in the cases rn, > 2 - 6/N+4 (N >= 3). If the flow of fluid is ignored, our result is consistent with and improves the result of Tao, Winkler ([15]) and Tao, Winkler ([11), who proved the possibility of global boundedness, in the case that N = 2,m > 1 and N = 3, m > 8/7, respectively.
