We consider the parabolic–elliptic chemotaxis-growth system
under no-flux boundary conditions in a smoothly bounded domain , e9b35aa8249ff094dedbb7789a518" title="Click to view the MathML source">N≥1, where χ,μ,m,α and e56c06a360e25c135adb9f4" title="Click to view the MathML source">γ are prescribed positive parameters fulfilling e938fea97002af04ae0ef3531f560" title="Click to view the MathML source">m≥1 and a0e93d8a58aeb596a6" title="Click to view the MathML source">γ≥1.
Recently, it has been proved in Galakhov et al. (2016) that if either α>m+γ−1 or α=m+γ−1 and a64762">, for any given bcbf79cea95fcf08e94c26471"> this system possesses a global and bounded classical solution. The present work further shows that the same conclusion still holds for the critical case α=m+γ−1 and a6c1c04e7e9db5a">.