On new characterization of inextensible flows of space-like curves in de Sitter space

Mustafa Yeneroğlu

Displaying similar documents to “On new characterization of inextensible flows of space-like curves in de Sitter space”

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial. ...

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Free convection flow of water at $4^{\circ} C$ past an infinite porous plate with constant suction

V. M. Soundalgekar (1975)

Matematički Vesnik

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An attraction result and an index theorem for continuous flows on $ℝ^{n} \times [0, \infty)$

Klaudiusz Wójcik (1997)

Annales Polonici Mathematici

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We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n + 1}$ for which $\partial E = ℝ^{n} \times 0$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^{n} \times [0, \infty)$ .

Scattering for 1D cubic NLS and singular vortex dynamics

Valeria Banica, Luis Vega (2012)

Journal of the European Mathematical Society

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We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions $χ_{a} (t, x)$ form a family of evolving regular curves in $ℝ^{3}$ that develop a singularity in finite time, indexed by a parameter $a > 0$ . We consider curves that are small regular perturbations of $χ_{a} (t_{0}, x)$ for a fixed time $t_{0}$ . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of...

Polynomial decay of correlations for a class of smooth flows on the two torus

Bassam Fayad (2001)

Bulletin de la Société Mathématique de France

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Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a $t^{- η}$ -speed of mixing, for some $η > 0$ .

Ricci flow coupled with harmonic map flow

Reto Müller (2012)

Annales scientifiques de l'École Normale Supérieure

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We investigate a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $φ$ from $M$ to some closed target manifold $N$ , $\frac{\partial}{\partial t} g = - 2 Rc + 2 α \nabla φ \otimes \nabla φ, \frac{\partial}{\partial t} φ = τ_{g} φ,$ where $α$ is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of $φ$ a-priori by choosing $α$ large enough. Moreover, it suffices to bound the curvature...

A second order unconditionally positive space-time residual distribution method for solving compressible flows on moving meshes

Dobeš, Jiří, Deconinck, Herman

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A space-time formulation for unsteady inviscid compressible flow computations in 2D moving geometries is presented. The governing equations in Arbitrary Lagrangian-Eulerian formulation (ALE) are discretized on two layers of space-time finite elements connecting levels $n$ , $n + 1 / 2$ and $n + 1$ . The solution is approximated with linear variation in space (P1 triangle) combined with linear variation in time. The space-time residual from the lower layer of elements is distributed to the nodes at level...

Numerical comparison of unsteady compressible viscous flow in convergent channel

Pořízková, Petra, Kozel, Karel, Horáček, Jaromír

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This study deals with a numerical solution of a 2D flows of a compressible viscous fluids in a convergent channel for low inlet airflow velocity. Three governing systems – Full system, Adiabatic system, Iso-energetic system $b a s e d o n t h e N a v i e r - S t o k e s e q u a t i o n s f o r l a m i n a r f l o w a r e t e s t e d . T h e n u m e r i c a l s o l u t i o n i s r e a l i z e d b y f i n i t e v o l u m e m e t h o d a n d t h e p r e d i c t o r - c o r r e c t o r M a c C o r m a c k s c h e m e w i t h J a m e s o n a r t i f i c i a l v i s c o s i t y u s i n g a g r i d o f q u a d r i l a t e r a l c e l l s . T h e u n s t e a d y g r i d o f q u a d r i l a t e r a l c e l l s i s c o n s i d e r e d i n t h e f o r m o f c o n s e r v a t i o n l a w s u s i n g A r b i t r a r y L a g r a n g i a n - E u l e r i a n m e t h o d . T h e n u m e r i c a l r e s u l t s, a c q u i r e d f r o m a d e v e l o p e d p r o g r a m, a r e p r e s e n t e d f o r i n l e t v e l o c i t y$ u=4.12 ms-1 $a n d R e y n o l d s n u m b e r R e =$ 4 103 $.$

On embeddability of automorphisms into measurable flows from the point of view of self-joining properties

Joanna Kułaga-Przymus (2015)

Fundamenta Mathematicae

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We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic is 2-fold quasi-simple (resp. 2-fold distally simple) if and only if T₁ is 2-fold quasi-simple (resp. 2-fold distally simple). We also show that the Furstenberg-Zimmer decomposition for a flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic with respect to any flow factor is the same for ${(T_{t})}_{t \in ℝ}$ and for T₁. We give an example of a 2-fold quasi-simple flow disjoint from simple flows and whose time-one...

Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

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Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved $L^{q}$ -estimates of second order derivatives uniformly in the angular and translational velocities,...

Generalized gradient flow and singularities of the Riemannian distance function

Piermarco Cannarsa (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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Significant information about the topology of a bounded domain $Ω$ of a Riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial Ω}$ , from the boundary of $Ω$ . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of $d_{\partial Ω}$ , as well as applications to homotopy equivalence.

Global existence of solutions for incompressible magnetohydrodynamic equations

Wisam Alame, W. M. Zajączkowski (2004)

Applicationes Mathematicae

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Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain Ω ⊂ ℝ³ with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to $W_{p}^{2, 1} (Ω \times (0, T))$ and the pressure q satisfies $\nabla q \in L_{p} (Ω \times (0, T))$ for p ≥ 7/3.

$L^{q}$ -approach to weak solutions of the Oseen flow around a rotating body

Stanislav Kračmar, Šárka Nečasová, Patrick Penel (2008)

Banach Center Publications

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We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in $L^{q}$ -spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions...

Three examples of brownian flows on $ℝ$

Yves Le Jan, Olivier Raimond (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We show that the only flow solving the stochastic differential equation (SDE) on $ℝ$ $d X_{t} = 1_{{X_{t} g t; 0}} W^{+} (d t) + 1_{{X_{t} l t; 0}} d W^{-} (d t),$ where $W^{+}$ and $W^{-}$ are two independent white noises, is a coalescing flow we will denote by $ϕ^{\pm}$ . The flow $ϕ^{\pm}$ is a Wiener solution of the SDE. Moreover, $K^{+} = 𝖤 [δ_{ϕ^{\pm}} | W^{+}]$ is the unique solution (it is also a Wiener solution) of the SDE $K_{s, t}^{+} f (x) = f (x) + \int_{s}^{t} K_{s, u} (1_{ℝ}^{+} f^{'}) (x) W^{+} (d u) + \frac{1}{2} \int_{s}^{t} K_{s, u} f ` ` (x) d u$ for $s l t; t$ , $x \in ℝ$ and $f$ a twice continuously differentiable function. A third flow $ϕ^{+}$ can be constructed out of the $n$ -point motions of $K^{+}$ . This flow is coalescing and its $n$ -point motion...

On Schrödinger maps from $T^{1}$ to $S^{2}$

Robert L. Jerrard, Didier Smets (2012)

Annales scientifiques de l'École Normale Supérieure

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We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from $T^{1}$ to $S^{2} .$ This estimate yields some continuity properties of the flow map for the topology of $L^{2} (T^{1}, S^{2})$ , provided one takes its quotient by the continuous group action of $T^{1}$ given by translations. We also prove that without taking this quotient, for any $t > 0$ the flow map at time $t$ is discontinuous as a map from $𝒞^{\infty} (T^{1}, S^{2})$ , equipped with the weak topology of $H^{1 / 2},$ to the space of distributions ${(𝒞^{\infty} (T^{1}, ℝ^{3}))}^{*} .$ The argument relies...

Relaxation of the incompressible porous media equation

László Székelyhidi Jr (2012)

Annales scientifiques de l'École Normale Supérieure

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It was shown recently by Córdoba, Faraco and Gancedo in [1] that the 2D porous media equation admits weak solutions with compact support in time. The proof, based on the convex integration framework developed for the incompressible Euler equations in [4], uses ideas from the theory of laminates, in particular $T 4$ configurations. In this note we calculate the explicit relaxation of IPM, thus avoiding $T 4$ configurations. We then use this to construct weak solutions to the unstable interface...

The Kähler Ricci flow on Fano manifolds (I)

Xiuxiong Chen, Bing Wang (2012)

Journal of the European Mathematical Society

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We study the evolution of pluri-anticanonical line bundles $K_{M}^{- ν}$ along the Kähler Ricci flow on a Fano manifold $M$ . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of $M$ . For example, the Kähler Ricci flow on $M$ converges when $M$ is a Fano surface satisfying $c_{1}^{2} (M) = 1$ or $c_{1}^{2} (M) = 3$ . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism...

About the Calabi problem: a finite-dimensional approach

H.-D. Cao, J. Keller (2013)

Journal of the European Mathematical Society

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Let us consider a projective manifold $M^{n}$ and a smooth volume form $Ω$ on $M$ . We define the gradient flow associated to the problem of $Ω$ -balanced metrics in the quantum formalism, the $Ω$ -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the $Ω$ -balancing flow converges towards a natural flow in Kähler geometry, the $Ω$ -Kähler flow. We also prove the long time existence of the $Ω$ -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing...

Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends

Tatsuhiko Yagasaki (2007)

Fundamenta Mathematicae

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Suppose M is a noncompact connected n-manifold and ω is a good Radon measure of M with ω(∂M) = 0. Let ℋ(M,ω) denote the group of ω-preserving homeomorphisms of M equipped with the compact-open topology, and $ℋ_{E} (M, ω)$ the subgroup consisting of all h ∈ ℋ(M,ω) which fix the ends of M. S. R. Alpern and V. S. Prasad introduced the topological vector space (M,ω) of end charges of M and the end charge homomorphism $c^{ω} : ℋ_{E} (M, ω) \to (M, ω)$ , which measures for each $h \in ℋ_{E} (M, ω)$ the mass flow toward ends induced by h. We show that the...