A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity. (16th April 2015) - Lankeit, Johannes
Abstract : We consider the parabolic chemotaxis model u t = Δu − χ ∇ · u v ∇ v v t = Δv − v + u in a smooth, bounded, convex two‐dimensional domain and show global existence and boundedness of solutions for χ ∈(0, χ 0 ) for some χ 0 >1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional F a, b ( u, v ) = ∫ Ω u ln u − a ∫ Ω u ln v + b ∫ Ω ∇ v 2 for a > 0, b ≥0, where using nonzero values of b appears to be new in this context. Copyright © 2015 John Wiley & Sons, Ltd.