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Well-posedness for a class of non-Newtonian fluids with general growth conditions

Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska, Andrzej Warzyński (2009)

Banach Center Publications

The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with...

Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).

Tosio Kato, Gustavo Ponce (1986)

Revista Matemática Iberoamericana

In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.

Weyl Numbers in Function Spaces.

António M. Caetano (1990)

Forum mathematicum

Weyl Numbers in Function Spaces II.

António M. Caetano (1991)

Forum mathematicum

Weyl numbers versus Z-Weyl numbers

Bernd Carl, Andreas Defant, Doris Planer (2014)

Studia Mathematica

Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), the s-number sequence of Z-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with Z-Weyl numbers-a problem originally posed by A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue distribution...

What is a disk?

Kari Hag (1999)

Banach Center Publications

This paper should be considered as a companion report to F.W. Gehring’s survey lectures “Characterizations of quasidisks” given at this Summer School [7]. Notation, definitions and background results are given in that paper. In particular, D is a simply connected proper subdomain of $R^{2}$ unless otherwise stated and D* denotes the exterior of D in ${\bar{R}}^{2}$ . Many of the characterizations of quasidisks have been motivated by looking at properties of euclidean disks. It is therefore natural to go back and ask...

What is "local theory of Banach spaces"?

Albrecht Pietsch (1999)

Studia Mathematica

Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.

Wheeling around von Neumann-Jordan constant in Banach spaces

J. Alonso, P. Martín, P. L. Papini (2008)

Studia Mathematica

In recent times, many constants in Banach spaces have been defined and/or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been devoted to organize all connections, also because the literature on the subject is growing at an always bigger rate. Here we give some new connections which better the insight on some of them. In particular, we improve a known inequality between the von Neumann-Jordan and James constants.

When a composition algebra is barrelled?

Jorge Bustamante González, Raúl Escobedo Conde (1997)

Extracta Mathematicae

When a unital F-algebra has all maximal left (right) ideals closed?

W. Żelazko (2006)

Studia Mathematica

We prove that a real or complex unital F-algebra has all maximal left ideals closed if and only if the set of all its invertible elements is open. Consequently, such an algebra also automatically has all maximal right ideals closed.

When does bvca (...,X) Contain a Copy of l... ?

Juan Carlos Ferrando (1994)

Mathematica Scandinavica

When does finite holomorphy imply holomorphy?

Nachbin, Leopoldo (1994)

Portugaliae Mathematica

When $(E, σ (E, E^{'}))$ is a $D F$ -space?

Dorota Krassowska, Wiesƚaw Śliwa (1992)

Commentationes Mathematicae Universitatis Carolinae

Let $(E, t)$ be a Hausdorff locally convex space. Either $(E, σ (E, E^{'}))$ or $(E^{'}, σ (E^{'}, E))$ is a $D F$ -space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].

When is a quantum space not a group?

Piotr Mikołaj Sołtan (2010)

Banach Center Publications

We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as properties...

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

Let $ℛ_{α}$ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $α \in ℂ$ . I give an elementary proof of the necessary and sufficient condition for $ℛ_{α}$ to be a locally finite complex measure (= complex Radon measure).

When is L(X) topologizable as a topological algebra?

W. Żelazko (2002)

Studia Mathematica

Let X be a locally convex space and L(X) be the algebra of all continuous endomorphisms of X. It is known (Esterle [2], [3]) that if L(X) is topologizable as a topological algebra, then the space X is subnormed. We show that in the case when X is sequentially complete this condition is also sufficient. In this case we also obtain some other conditions equivalent to the topologizability of L(X). We also exhibit a class of subnormed spaces X, called sub-Banach spaces, which are not necessarily sequentially...

When is there a discontinuous homomorphism from L¹(G)?

Volker Runde (1994)

Studia Mathematica

Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.

When some variational properties force convexity

M. Volle, J.-B. Hiriart-Urruty, C. Zălinescu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest...

When the topology of and infinite-dimensional Banach space coincides with a Hilbert space topology

M. Mączyński (1974)

Studia Mathematica

When unit groups of continuous inverse algebras are regular Lie groups

Helge Glöckner, Karl-Hermann Neeb (2012)

Studia Mathematica

It is a basic fact in infinite-dimensional Lie theory that the unit group $A^{\times}$ of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group $A^{\times}$ is regular in Milnor’s sense. Notably, $A^{\times}$ is regular if A is Mackey-complete and locally m-convex.

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