On the existence of local strong solutions to chemotaxis–shallow water system with large data and vacuum

Che, Jiahang; Chen, Li; Duan, Ben; Luo, Zhen

doi:10.1016/j.jde.2016.09.005

Cited by 16 publications

(12 citation statements)

References 38 publications

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“…We state the local existence and uniqueness theorem for the solution of the system (1)-(3) here. One can see the proof in [4] and [22].…”

Section: Corollary 1 For the Functionmentioning

confidence: 92%

“…in space-time domain R 2 × (0, ∞). This system was derived in [4] to model the dynamics of the oxygen and aerobic bacteria in a viscous fluid with free surface. Here we denote the unknown bacterial density, the chemoattractant concentration, the fluid height and the fluid velocity field by n, c, h, u, respectively.…”

mentioning

confidence: 99%

“…While for the three dimensional case, Winkler [29][30] obtained the global existence of weak solutions and then showed that this weak solutions become smooth after a waiting time and uniformly converged in the large-time limit when χ and f are sufficiently smooth given functions. We also refer to [ Considering the two important facts that the cells stay at the surface of the fluid and the vertical acceleration of the fluid can be neglected, the authors in [4] derived the two-dimensional chemotaxis-shallow water system (1) from the chemotaxis-Navier-Stokes system (4). This coupled shallow water type chemotactic model presents a kind of chemotaxis-compressible fluid, which not only consists of chemotaxis and diffusion mechanism, but also includes transport and conservation laws.…”

mentioning

confidence: 99%

“…Up to now, there are only few analytic results on the solvability of corresponding initial(-boundary)-value problems. In [4], the authors first established the local strong solution and blow up criterion under the large initial data allowing vacuum. Tao and Yao [22] proved the global well-posedness of strong solution and investigated the asymptotic behavior of the global solution.…”

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confidence: 99%

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Global classical solutions to two-dimensional chemotaxis-shallow water system

Yang¹

2021

DCDS-B

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“…We state the local existence and uniqueness theorem for the solution of the system (1)-(3) here. One can see the proof in [4] and [22].…”

Section: Corollary 1 For the Functionmentioning

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Global classical solutions to two-dimensional chemotaxis-shallow water system

Yang¹

2021

DCDS-B

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“…Recently, the chemotaxis process in fluid has been studied (see [12,21,22,40,41,49,53]). The possible effects result from the interaction of chemotactic and fluid transport process.…”

Section: Introductionmentioning

confidence: 99%

Suppression of blow up by mixing in generalized Keller–Segel system with fractional dissipation

Shi

Wang

2020

Communications in Mathematical Sciences

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In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with a fractional dissipation and advection by a weakly mixing (see Definition 2.4). Here the attractive kernel has strong singularity, namely, the derivative appears in the nonlinear term by singular integral. Without advection, the solution of equation blows up in finite time. Under a suitable mixing condition on the advection, we show the global existence of classical solution with large initial data in the case of the derivative of dissipative term is higher than that of nonlinear term. Since the attractive kernel is strong singularity, the weakly mixing has destabilizing effect in addition to the enhanced dissipation effect, which makes the problem more complicated and difficult. In this paper, we establish the L ∞ -criterion and obtain the global L ∞ estimate of the solution through some new ideas and techniques. Combined with [48], we discuss all cases of generalized Keller-Segel system with mixing effect, which was proposed by Kiselev, Xu (see [36]) and Hopf, Rodrigo (see [31]). Based on more precise estimate of solution and the resolvent estimate of semigroup operator, we introduce a new method to study the enhanced dissipation effect of mixing in generalized parabolic-elliptic Keller-Segel equation with a fractional dissipation. And the RAGE theorem is no longer needed in our analysis.

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Global Smooth Solution for Navier–Stokes/Poisson–Nernst–Planck System in $${\mathbb {R}}^{2}$$

Wang

2023

J. Math. Fluid Mech.

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On the existence of local strong solutions to chemotaxis–shallow water system with large data and vacuum

Cited by 16 publications

References 38 publications

Global classical solutions to two-dimensional chemotaxis-shallow water system

Global classical solutions to two-dimensional chemotaxis-shallow water system

Suppression of blow up by mixing in generalized Keller–Segel system with fractional dissipation

Global Smooth Solution for Navier–Stokes/Poisson–Nernst–Planck System in $${\mathbb {R}}^{2}$$

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