| Chemotaxis,the directed movement of cells or organisms in response to chemical stimuli,plays essential roles in various biological processes such as embryonic development,wound healing,and disease progression.It is important for bacteria to find food?glucose?by swimming toward the highest concentration of food molecules,or to flee from poisons.Somatic cells,bacteria and other single or multicellular organisms,according to certain chemical substances in the environment,determine their direction of movement.Chemical attractants and chemical rejectants are determined by the effects of inorganic or organic substances that control chemotaxis in swimmers.The action of chemical attractants is caused by the description or hypothesis of chemotactic receptors,and the response to chemical exclusion leads to axial swim,which are considered to be a basic dynamic phenomenon in bacteria.We consider the attraction-repulsion chemotaxis system with rotational flux terms where ? ? R2 is a bounded domain with smooth boundary.Here S1 and S2are given parameter functions on [0,?)2× ? with values in R2×2.It is shown that for any choice of suitably regular initial data?u0,v0,w0?fulfilling a smallness condition on the norm of v0,w0 in L????,the corresponding initial-boundary value problem possesses a global bounded classical solution.Firstly,we prove the local existence of this solution,and then consider the existence of the solution of the corresponding attraction-repulsion chemotaxis model in the case of S1= 0 and S2= 0 on ? ?,and give some important a priori estimates.For the general matrix value functions S1 and S2,we obtain the global existence of the classical solution by using the approximation method. |
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