Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Kerui Jiang, Zuhan Liu, Ling ZhouAbstractIn this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates.

Source: Nonlinear Analysis: Real World Applications - February 8, 2020 Category: Research Source Type: research