Displaying similar documents to “Interior C 1 , α -Regularity of Weak Solutions to the Equations of Stationary Motions of Certain Non-Newtonian Fluids in Two Dimensions”

Cauchy problem for the non-newtonian viscous incompressible fluid

Milan Pokorný (1996)

Applications of Mathematics

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We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor τ V ( 𝕖 ) = τ ( 𝕖 ) - 2 μ 1 Δ 𝕖 , where the nonlinear function τ ( 𝕖 ) satisfies τ i j ( 𝕖 ) e i j c | 𝕖 | p or τ i j ( 𝕖 ) e i j c ( | 𝕖 | 2 + | 𝕖 | p ) . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for p > 1 for both models. Then, under vanishing higher viscosity μ 1 , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for p > 3 n n + 2 , its uniqueness...

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...

On Relative γ k -Sets

Maddalena Bonanzinga, Filippo Cammaroto, Bruno A. Pansera (2007)

Bollettino dell'Unione Matematica Italiana

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In this note we show a relative version of γ k -set introduced and studied in [12]. We give several characterizations of this property; in particular one of the characterizations is Ramsey theoretical. Also we give a result involving a property of the corresponding mapping between function spaces.

The subspace of weak P -points of *

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let W be the subspace of * consisting of all weak P -points. It is not hard to see that W is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that W is a p -pseudocompact space for all p * .

A New L 1 -Lower Semicontinuity Result

Daniele Graziani (2007)

Bollettino dell'Unione Matematica Italiana

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The aim of this work is to prove a chain rule and an L 1 -lower semicontinuity theorems for integral functional defined on B V ( Ω ) . Moreover we apply this result in order to obtain new relaxation and Γ -convergence result without any coerciveness and any continuity assumption of the integrand f ( x , s , p ) with respect to the variable s .

Conductor and separating degrees for sets of points in r and in 1 × 1

Lucia Marino (2006)

Bollettino dell'Unione Matematica Italiana

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We attempt to generalize conductor degree's results, known in 2 , to the case of 0-dimensional schemes of r . In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in r and we determine the conductor degree of every point in a r -partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...

Correctors for Parabolic Equations in a Heterogeneous Fibered Medium

Mourad Sfaxi, Ali Sili (2007)

Bollettino dell'Unione Matematica Italiana

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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium Ω made of two materials. The first one is located in a set F ϵ of cylindrical parallel fibers periodically distributed with a period of size ϵ , and the second one is located in the "matrix" M ϵ = Ω F ϵ . The ratio between the conductivity coefficients of the two materials is of order 1 / ϵ 2 . After writing the homogenized problem, we give a corrector result and prove...

Relaxation and gamma-convergence of supremal functionals

Francesca Prinari (2006)

Bollettino dell'Unione Matematica Italiana

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We prove that the Γ -limit in L μ of a sequence of supremal functionals of the form F k ( u ) = μ - ess sup Ω f k ( x , u ) is itself a supremal functional. We show by a counterexample that, in general, the function which represents the Γ -lim F ( , B ) of a sequence of functionals F k ( u , B ) = μ - ess sup B f k ( x , u ) can depend on the set B and wegive a necessary and sufficient condition to represent F in the supremal form F ( u , B ) = μ - ess sup B f ( x , u ) . As a corollary, if f represents a supremal functional, then the level convex envelope of f represents its weak* lower semicontinuous envelope. ...

A Regular Threefold of General Type with p g = 0 and P 2 = 6

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus P 2 is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with p g = 0 : The examples in the literature have P 2 5 . In the present paper we present a non-singular threefold with p g = q 1 = q 2 = 0 ; P 2 = 6 ; the bicanonical map is stably birational.

A Note on -Maps

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

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Richness of the class of -maps [3] is investigated. Several consequences for the theory of quasi- -closed spaces are indicated.

Some Separation Axioms Via Ideals

D. Sivaraj, V. Renuka Devi (2007)

Bollettino dell'Unione Matematica Italiana

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We introduce a new class of spaces, called Hausdorff modulo or T 2 mod spaces with respect to an ideal which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic....

Isomorphisms of Royden Type Algebras Over 𝕊 1

Teresa Radice, Eero Saksman, Gabriella Zecca (2009)

Bollettino dell'Unione Matematica Italiana

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Let 𝕊 1 and 𝔻 be the unit circle and the unit disc in the plane and let us denote by 𝒜 ( 𝕊 1 ) the algebra of the complex-valued continuous functions on 𝕊 1 which are traces of functions in the Sobolev class W 1 , 2 ( 𝔻 ) . On 𝒜 ( 𝕊 1 ) we define the following norm u = u L ( 𝕊 1 ) + ( 𝔻 | u ~ | 2 ) 1 / 2 where is the harmonic extension of u to 𝔻 . We prove that every isomorphism of the functional algebra 𝒜 ( 𝕊 1 ) is a quasitsymmetric change of variables on 𝕊 1 .

Global regularity for the 3D MHD system with damping

Zujin Zhang, Xian Yang (2016)

Colloquium Mathematicae

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We study the Cauchy problem for the 3D MHD system with damping terms ε | u | α - 1 u and δ | b | β - 1 b (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.

On locally S -closed spaces

Takashi Noiri (1983)

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

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente S -chiuso sia localmente S -chiuso.

A uniqueness result for the continuity equation in two dimensions

Giovanni Alberti, Stefano Bianchini, Gianluca Crippa (2014)

Journal of the European Mathematical Society

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We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation t u + . ˙ ( b u ) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b . As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain non-autonomous vector fields b with...

Semicontinuity in L for polyconvex integrals

Emilio Acerbi, Giuseppe Buttazzo, Nicola Fusco (1982)

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

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Viene studiata la semicontinuità rispetto alla topologia di L ( Ω ; 𝐑 m ) per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.

On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

Agnieszka Kałamajska (2001)

Colloquium Mathematicae

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We study the functional I f ( u ) = Ω f ( u ( x ) ) d x , where u=(u₁, ..., uₘ) and each u j is constant along some subspace W j of ℝⁿ. We show that if intersections of the W j ’s satisfy a certain condition then I f is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on W j j = 1 , . . . , m to have the equivalence: I f is weakly continuous if and only if f is Λ-affine.

Three examples of brownian flows on

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 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 ± . The flow ϕ ± is a Wiener solution of the SDE. Moreover, K + = 𝖤 [ δ ϕ ± | W + ] is the unique solution (it is also a Wiener solution) of the SDE K s , t + f ( x ) = f ( x ) + s t K s , u ( 1 + f ' ) ( x ) W + ( d u ) + 1 2 s t K s , u f ` ` ( x ) d u for s l t ; t , x 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 weak i -homotopy equivalences of modules

Zheng-Xu He (1984)

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

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Si definisce il gruppo di i —omotopia di un singolo modulo e si introduce la nozione di equivalenza i -omotopica debole. Sotto determinate condizioni per l'anello di base Λ oppure per i moduli considerati, le equivalenze i -omotopiche deboli coincidono con le equivalenze i -omotopiche (forti).

L p Regularity of Transmission Problems in Dihedral Domains

Aissa Aibeche, Wided Chikouche, Serge Nicaise (2007)

Bollettino dell'Unione Matematica Italiana

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We consider the transmission problem for the Laplace operator in a straight cylinder with data in L p . Applying the theory of the sums of operators in Banach spaces, we prove that the solution admits a decomposition into a regular part in W 2 , p and an explicit singular part.

A Note on Sectorial and R-Sectorial Operators

Alberto Venni (2008)

Bollettino dell'Unione Matematica Italiana

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The following results are proved: (i) if α , β + and A is a sectorial operator, then the set { t α A β ( t + A ) ; t > 0 } is bounded; (ii) the same set of operators is R-bounded if A is R-sectorial.

A Montel Type Result for Subharmonic Functions

R. Supper (2009)

Bollettino dell'Unione Matematica Italiana

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This article is devoted to sequences ( u n ) n of subharmonic functions in N , with finite order, whose means J u n ( r ) (over spheres centered at the origin, with radius r) satisfy such a condition as: r > 0 , A r > 0 such that J u n ( r ) A r , n 𝐍 . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let D be an integral domain with quotient field D . Recall that D is Schreier if D is integrally closed and for all x , y , z D { 0 } , x | y z implies that x = r s where r | y e s | z . A GCD domain is Schreier. We show that an integral domain D is a GCD domain if and only if (i) for each pair a , b D { 0 } , there is a finitely generated ideal B such that a D b D = B v and (ii) every quadratic in D [ X ] that is a product of two linear polynomials in K [ X ] is a product of two linear polynomials in D [ X ] . We also show that D is Schreier if and only if every...

Eisenstein ideal and reducible λ -adic Representations Unramified Outside a Finite Number of Primes.

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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The object of this note is to study certain 2-dimensional λ -adic representations of Gal ( Q ¯ / Q ) ; fixed p 1 , , p n distinct primes, we will consider representations ρ : G G L 2 ( A ) , given by the matrix ρ = ( a b c d ) which are unramified outside p 1 , , p n , and the residue characteristic of λ , which are a product of m representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo λ . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...

Degenerate Elliptic Equations and Morrey Spaces

Francesco Borrello (2007)

Bollettino dell'Unione Matematica Italiana

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In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation L u X i * ( a i j X j u ) = f . where X 1 , X 2 , , X m are vector fields satisfying Hörmander condition and a i j L . We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case f 0 we are able to give necessary condition too.