Global weak solutions and eventual smoothness in a 3D two‐competing‐species chemotaxis‐Navier‐Stokes system with two consumed signals
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6154
Abstract: This paper deals with a two‐competition‐species chemotaxis‐Navier‐Stokes system with two different consumed signals (n1)t+u·∇n1=d1Δn1−χ1∇·(n1∇c)+μ1n1(1−n1−a1n2),inΩ×(0,∞),ct+u·∇c=d2Δc−α1cn2,inΩ×(0,∞),(n2)t+u·∇n2=d3Δn2−χ2∇·(n2∇v)+μ2n2(1−a2n1−n2),inΩ×(0,∞),vt+u·∇v=d4Δv−α2vn1,inΩ×(0,∞),ut+(u·∇)u=Δu+∇P+(β1n1+β2n2)∇ϕ,inΩ×(0,∞),∇·u=0,inΩ×(0,∞), in a smooth bounded domain Ω⊂R3 under zero Neumann boundary conditions for n1,n2,c,v , and homogeneous Dirichlet boundary condition for u… read more here.
Keywords: system; navier stokes; species chemotaxis; weak solutions ... See more keywords
Regularity Criteria for the Axisymmetric Navier–Stokes System with Negative Weights
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DOI: 10.1007/s00025-019-1059-y
Abstract: As is well-known, for the axisymmetric Navier–Stokes equations, $$ru^{\theta }$$ obeys a maximal principle, $$\left\| ru^{\theta }(t)\right\| _{L^\infty } \leqslant \left\| ru^{\theta }_0\right\| _{L^\infty }$$. Utilizing this fact, we can establish some more weighted regularity… read more here.
Keywords: stokes system; criteria axisymmetric; regularity criteria; regularity ... See more keywords
An Adaptive SDG Method for the Stokes System
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DOI: 10.1007/s10915-016-0265-y
Abstract: Staggered grid techniques are attractive ideas for flow problems due to their more enhanced conservation properties. Recently, a staggered discontinuous Galerkin method is developed for the Stokes system. This method has several distinctive advantages, namely… read more here.
Keywords: discontinuous galerkin; method; staggered discontinuous; galerkin method ... See more keywords
Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method
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DOI: 10.1016/j.cma.2018.04.017
Abstract: Abstract In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to… read more here.
Keywords: diagonalization method; stokes system; fast diagonalization;
Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion
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DOI: 10.1016/j.jde.2019.11.078
Abstract: Abstract In this paper, a chemotaxis-Stokes system with slow p-Laplacian diffusion { n t + u ⋅ ∇ n = ∇ ⋅ ( | ∇ n | p − 2 ∇ n ) − ∇… read more here.
Keywords: system slow; chemotaxis stokes; slow laplacian; laplacian diffusion ... See more keywords
The general magneto-static model and Maxwell-Stokes system with topological parameters
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DOI: 10.1016/j.jde.2020.09.002
Abstract: Abstract In this paper we study a nonlinear magneto-static model on a general domain in R 3 which is multiply-connected and has holes, and under a nonlinear relation between the magnetic induction B and the… read more here.
Keywords: static model; stokes system; maxwell stokes; topology ... See more keywords
Global bounded weak solutions for a chemotaxis-Stokes system with nonlinear diffusion and rotation
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DOI: 10.1016/j.jde.2021.04.020
Abstract: Abstract In this paper, we discuss the following chemotaxis-Stokes system with nonlinear diffusion and rotation { n t + u ⋅ ∇ n = Δ n m − ∇ ⋅ ( n S ( x… read more here.
Keywords: nonlinear diffusion; stokes system; chemotaxis stokes; system nonlinear ... See more keywords
Stability of singular solutions to the Navier-Stokes system
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DOI: 10.1016/j.jde.2022.01.010
Abstract: We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem… read more here.
Keywords: solutions navier; navier stokes; stokes system; singular solutions ... See more keywords
On the nonstationary Stokes system in a cone: Asymptotics of solutions at infinity
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DOI: 10.1016/j.jmaa.2019.123821
Abstract: The paper deals with the Dirichlet problem for the nonstationary Stokes system in a cone. The authors obtain existence and uniqueness results for solutions in weighted Sobolev spaces and study the asymptotics of the solutions… read more here.
Keywords: asymptotics solutions; nonstationary stokes; solutions infinity; stokes system ... See more keywords
Global classical solutions in a chemotaxis(-Navier)-Stokes system with indirect signal production
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DOI: 10.1016/j.jmaa.2021.125299
Abstract: Abstract In this paper, we study the initial-boundary value problem for the coupled chemotaxis(-Navier)-Stokes system with indirect signal production { ∂ t n + u ⋅ ∇ n = Δ n − ∇ ⋅ (… read more here.
Keywords: system; stokes system; indirect signal; system indirect ... See more keywords
Optimal well-posedness for the pressureless Euler–Navier–Stokes system
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DOI: 10.1063/5.0136429
Abstract: In this work, we investigate the Cauchy problem for the pressureless Euler–Navier–Stokes system in R3. We first establish the global small solutions of this system with critical regularity and then obtain the optimal time decay… read more here.
Keywords: system; pressureless euler; navier stokes; euler navier ... See more keywords