Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems

We prove the global-in-time existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain of R² or R³ with initial chemical concentration small in H¹. No smallness assumption is imposed on the initial cell density which is in L². We first show that when the initial chemical concentration c₀ is small only in H¹ and (n₀−n∞,c₀) is smooth, the classical solution exists for all time. Then we construct weak solutions as limits of smooth solutions corresponding to mollified initial data. Finally we determine the asymptotic behavior of the global solutions. Copyright © 2015 Southwest Missouri State University.