Global weak solutions and eventual smoothness in a 3D two‐competing‐species chemotaxis‐Navier‐Stokes system with two consumed signals
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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
Two-Phase Solutions for One-Dimensional Non-convex Elastodynamics
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DOI: 10.1007/s00205-018-1326-1
Abstract: We explore the local existence and properties of classical weak solutions to the initial-boundary value problem for a class of quasilinear equations of elastodynamics in one space dimension with a non-convex stored-energy function, a model… read more here.
Keywords: phase; weak solutions; non convex; problem ... See more keywords
Stationary Solutions and Nonuniqueness of Weak Solutions for the Navier–Stokes Equations in High Dimensions
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DOI: 10.1007/s00205-019-01366-9
Abstract: Consider the unforced incompressible homogeneous Navier–Stokes equations on the d-torus $${\mathbb{T}^d}$$Td where $${d \geq 4}$$d≥4 is the space dimension. It is shown that there exist nontrivial steady-state weak solutions $${u \in L^{2} (\mathbb{T}^d)}$$u∈L2(Td). The result… read more here.
Keywords: stationary solutions; stokes equations; weak solutions; solutions nonuniqueness ... See more keywords
On the weak solutions to steady Navier-Stokes equations with mixed boundary conditions
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DOI: 10.1007/s00209-018-2072-7
Abstract: In this paper, for the Navier-Stokes equations in a bounded connected polygon or polyhedron $$\Omega \subset R^d$$Ω⊂Rd, $$d=2,3$$d=2,3, with a homogenous stress type mixed boundary condition, we establish an a priori estimate for the weak… read more here.
Keywords: stokes equations; weak solutions; mixed boundary; navier stokes ... See more keywords
Weak Solutions to the Navier–Stokes Inequality with Arbitrary Energy Profiles
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DOI: 10.1007/s00220-019-03588-0
Abstract: In a recent paper, Buckmaster and Vicol (Ann Math (2) 189(1):101–144, 2019 ) used the method of convex integration to construct weak solutions u to the 3D incompressible Navier–Stokes equations such that $$\Vert u(t) \Vert… read more here.
Keywords: energy; stokes inequality; weak solutions; navier stokes ... See more keywords
Regularity of Weak Solutions to the 3D Magneto-Micropolar Equations in Besov Spaces
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DOI: 10.1007/s10440-018-0220-z
Abstract: This paper deals with the regularity of weak solutions to the 3D magneto-micropolar fluid equations in Besov spaces. It is shown that for 0≤α≤1$0\le\alpha\le1$ if u∈L21+α(0,T;B˙∞,∞α)$u\in L^{\frac{2}{1+\alpha}}(0,T; \dot{B}_{\infty,\infty}^{\alpha})$, then the weak solution (u,ω,b)$(u,\omega ,b)$ is… read more here.
Keywords: regularity weak; besov spaces; magneto micropolar; weak solutions ... See more keywords
Convergence to Suitable Weak Solutions for a Finite Element Approximation of the Navier–Stokes Equations with Numerical Subgrid Scale Modeling
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DOI: 10.1007/s10915-016-0304-8
Abstract: In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality… read more here.
Keywords: solutions finite; finite element; convergence suitable; weak solutions ... See more keywords
Weak Solutions of Hopf Type to 2D Maxwell Flows with Infinite Number of Relaxation Times
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DOI: 10.1007/s10958-019-04264-3
Abstract: A system of equations describing the motion of fluids of Maxwell type is considered:∂∂tυ+υ⋅∇υ−∫0tKt−τdτ+∇p=fxt,diυυ=0.$$ \frac{\partial }{\partial t}\upsilon +\upsilon \cdot \nabla \upsilon -\underset{0}{\overset{t}{\int }}K\left(t-\tau \right) d\tau +\nabla p=f\left(x,t\right),\kern0.5em di\upsilon\;\upsilon =0. $$ Here K(t) is an exponential… read more here.
Keywords: type maxwell; weak solutions; maxwell flows; solutions hopf ... See more keywords
On Type I Blowups of Suitable Weak Solutions to the Navier–Stokes Equations Near Boundary
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DOI: 10.1007/s10958-021-05673-z
Abstract: In this note, boundary Type I blowups of suitable weak solutions to the Navier–Stokes equations are discussed. In particular, it has been shown that, under certain assumptions, the existence of nontrivial mild bounded ancient solutions… read more here.
Keywords: solutions navier; navier stokes; type blowups; weak solutions ... See more keywords
Weak Solutions to the Complex m-Hessian Equation on Open Subsets of $${{\mathbb {C}}}^{n}$$
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DOI: 10.1007/s11785-019-00948-5
Abstract: In this paper, we prove the existence of weak solutions to the complex m-Hessian equations in the class \({\mathcal {D}}_{m}(\Omega )\) on an open subset \(\Omega \) of \({\mathbb {C}}^n\). In the end of the… read more here.
Keywords: solutions complex; weak solutions; hessian equation; equation open ... See more keywords
Global weak solutions to the active hydrodynamics of liquid crystals
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DOI: 10.1016/j.jde.2019.10.020
Abstract: Abstract We consider the incompressible flow of the active hydrodynamics of liquid crystals with inhomogeneous density in the Beris-Edwards hydrodynamics framework. The Landau-de Gennes Q-tensor order parameter is used to describe the liquid crystalline ordering.… read more here.
Keywords: global weak; active hydrodynamics; hydrodynamics; liquid crystals ... See more keywords