RD-systems with chemotaxis: Global existence, boundedness, and blow-up of solutions

We study the finite time blow-up of solutions to general RD-systems with chemotaxis for multi-species. Our result shows that the blow-up is equivalent to the blow-up of the L(R)-norms of the solutions for r exceeding some critical value r(c). Under very loose conditions, we give the estimation of r(c), relying on a variant of Gagliardo-Nirenberg inequality, and a kind of bootstrap method which is very similar to the Alikakos-Moser iteration procedure.