Mathematical Models and Methods in Applied Sciences ( IF 3.6 ) Pub Date : 2023-07-06 , DOI: 10.1142/s0218202523400067 Wei Wang 1
We consider the chemotaxis-Navier–Stokes system with gradient-dependent flux limitation and nonlinear production: , , and in a bounded domain , where the flux limitation function and the signal production function generalize the prototypes and with , and . For the linear production case of , the global boundedness of solutions has been verified in the related literature for . In this paper, we expand to prove that the corresponding initial-boundary value problem possesses a unique globally bounded solution if for , or if for , which shows that when , that is, the self-enhancement ability of chemoattractant is weak, the solutions still remain globally bounded even though the flux limitation is relaxed to permit proper ; however, if , it is necessary to impose the stronger flux limitation than that in the case to inhibit the possible finite-time blow-up. This seems to be the first result on the global solvability in the chemotaxis-Navier–Stokes model with nonlinear production.
中文翻译:
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具有通量限制和非线性产生的二维趋化-纳维-斯托克斯系统中的全局有界性
我们考虑具有梯度相关通量限制和非线性产生的趋化-纳维-斯托克斯系统:,,和在有界域中,其中通量限制函数和信号产生函数概括原型和和,和。对于线性生产情况,解的全局有界性已在相关文献中得到验证。在本文中,我们扩展证明相应的初始边值问题具有唯一的全局有界解,如果为了, 或者如果为了,这表明当,即化学引诱剂的自我增强能力较弱,即使放宽通量限制以允许适当的解,解仍然保持全局有界; 然而,如果,有必要施加比情况更强的通量限制以抑制可能的有限时间爆炸。这似乎是具有非线性产生式的趋化-纳维-斯托克斯模型中全局可解性的第一个结果。