Reaction terms avoiding aggregation in slow fluids

Espejo, Elio; Suzuki, Takashi

doi:10.1016/j.nonrwa.2014.07.001

Cited by 76 publications

(52 citation statements)

References 19 publications

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“…for all t ∈ (0, T max ), and similarly, again by means of Young's inequality and (3.16), we obtain positive constants C 5 for all t ∈ (0, T max ). In estimating the boundary integrals in (3.14), we make use of the one-sided pointwise inequality…”

Section: Lemma 33 For Allsupporting

confidence: 59%

“…In (1.1), it is assumed that cell kinetics follows a logistic-type law determined by parameters r and μ, where allowing for the borderline case r = 0 we explicitly include cases when cell proliferation can be neglected. The model (1.1) moreover presupposes that in addition to the driving action of cells through buoyant forces within the gravitational field with potential φ, the motion of the fluid might be controlled by a given external force g. In particular, the system (1.1) therefore includes the outcomes of the modeling approaches for biomixing recently presented by Espejo and Suzuki [5] on the basis of an original work by Kiselev and Ryzhik [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Espejo and Suzuki [5] proved global existence of certain weak solutions for the particular two-dimensional version of (1.1) obtained by letting r = 0 and g = 0. Very recently, the global existence and large time behavior of classical solutions to a corresponding more complex Keller-Segel-Navier-Stokes system have been investigated in more detail in this two-dimensional context [22].…”

Section: Introductionmentioning

confidence: 99%

“…The limit case r = 0 becomes relevant when either the considered time scales are much smaller than those of cell proliferation, or when cells are a priori unable to reproduce themselves, such as e.g., in the model for broadcast spawning phenomena discussed in [5] and [13]. In such situations, the solution constructed in Theorem 1.1 enjoys the following decay properties.…”

Section: Introductionmentioning

confidence: 99%

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Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

Tao

Winkler

2015

Z. Angew. Math. Phys.

200

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The coupled chemotaxis-fluid systemis considered under no-flux boundary conditions for n and c and no-slip boundary conditions for u in three-dimensional bounded domains with smooth boundary, where r ≥ 0 and μ > 0 are given constants and φ ∈ W 1,∞ (Ω) and g ∈ C 1 (Ω × [0, ∞)) ∩ L ∞ (Ω × (0, ∞)) are prescribed parameter functions. It is shown that under the explicit condition μ ≥ 23 and suitable regularity assumptions on the initial data, the corresponding initial-boundary problem possesses a global classical solution which is bounded. Apart from this, it is proved that if r = 0, then both n(·, t) and c(·, t) decay to zero with respect to the norm in L ∞ (Ω) as t → ∞, and that if, moreover, ∞ 0 Ω |g| 2 < ∞, then also u(·, t) → 0 in L ∞ (Ω) as t → ∞.Mathematics Subject Classification. 35K55 · 35Q92 · 35Q35 · 92C17.

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Section: Lemma 33 For Allsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

Tao

Winkler

2015

Z. Angew. Math. Phys.

200

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“…(7) Lemma 2.2 (Gagliardo-Nirenberg Interpolation Inequality ; see [9], Proposition 3) Let , j k be any integers satisfying 0 , j k   and let 1 ,…”

Section: A Priori Estimatesmentioning

confidence: 99%

Global Existence of the Three Dimensional Heat-conductive Incompressible Viscous Fluids

2018

MATEC Web Conf.

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Abstract. In this paper, we consider the Cauchy problem of non-stationary motion of heatconducting incompressible viscous fluids in 3 . About the heat-conducting incompressible viscous fluids, there are many mathematical researchers study the variants systems when the viscosity and heat-conductivity coefficient are positive. For the heat-conductive system, it is difficulty to get the better regularity due to the gradient of velocity of fluid own the higher order term. It is hard to control it. In order to get its global solutions, we must obtain the a priori estimates at first, then using fixed point theorem, it need the mapping is contracted. We can get a local solution, then applying the criteria extension. We can extend the local solution to the global solutions. For the two dimensional case, the Gagliardo-Nirenberg interpolation inequality makes use of better than the three dimensional situation. Thus, our problem will become more difficulty to handle. In this paper, we assume the coefficient of viscosity is a constant and the coefficient of heat-conductivity satisfying some suitable conditions. We show that the Cauchy problem has a global-in-time strong solution ( , )

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Large time periodic solution to the coupled chemotaxis‐Stokes model

Chang

2017

Mathematische Nachrichten

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Reaction terms avoiding aggregation in slow fluids

Cited by 76 publications

References 19 publications

Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

Global Existence of the Three Dimensional Heat-conductive Incompressible Viscous Fluids

Large time periodic solution to the coupled chemotaxis‐Stokes model

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