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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...

Wiener amalgam spaces with respect to quasi-Banach spaces

Holger Rauhut (2007)

Colloquium Mathematicae

We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is new even for the classical Banach space case. To illustrate our theory we discuss in detail an example on the ax+b group.

Zeros of random functions in Bergman spaces

Joel H. Shapiro (1979)

Annales de l'institut Fourier

Suppose μ is a finite positive rotation invariant Borel measure on the open unit disc Δ , and that the unit circle lies in the closed support of μ . For 0 < p < ∞ the Bergman space A μ p is the collection of functions in L p ( μ ) holomorphic on Δ . We show that whenever a Gaussian power series f ( z ) = Σ ζ n a n z n almost surely lies in A μ p but not in ⋃ q > p A μ p , then almost surely: a) the zero set Z ( f ) of f is not contained in any A μ q zero set ( q > p , and b) Z ( f + 1 ) ∪ Z ( f - 1 ) is not contained in any A μ q zero set.

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