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In this paper, we study well-posedness, existence of a lower finite time blow-up bound and variants of controllability of the classical chemotaxis model inΩ  ×   (  0  ,  T  ){\Omega\times(0,T)}   , whereΩ  ⊂   ℝ  N{\Omega\subset\mathbb{R}^{N}}   ,N  =   1  ,  2  ,  3{N=1,2,3}   . The spatial domain restrictions allow the system with initial data inL  2   ⁢   (  Ω  ){L^{2}(\Omega)}    to admit a solution in

Well-posedness, blow-up dynamics and controllability of the classical chemotaxis model