In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in TriebelLizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the general...

A 'differential measure' is used to cast our calculus for the group SU (3) into a form similar to Schwinger's boson operator calculus for the group SU (2). It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.

We identify “spurious” states in meson-baryon scattering, those that appear in QCD for Nc > 3 but decouple for Nc = 3. The key observation is that the relevant flavor SU(3) Clebsch-Gordan coefficients contain factors of 1−3/Nc. We show that this method works even if SU(3) is badly broken. We also observe that resonant scattering poles lying outside naive quark model multiplets are not necessari...

Clebsch 1'2) was the first to derive, in 1859, the hydrodynamic equations for an ideal fluid from a variational principle for Euler coordinates. His derivation was, however, restricted to the case of an incompressible fluid. Later Bateman 3) showed that the analysis of Clebsch also applies to compressible fluids if the pressure is a function of density alone. Finally, in 1968, Seliger and Whith...

Abstract An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those were previously parameterized an arbitrary function  of materi...

In this paper, we show that a closed-form formula for the generalized Clebsch–Gordan integral and Fourier–Legendre expansion theory allow to evaluate hypergeometric series involving powers of normalized central binomial coefficient $${\frac{1}{4^{n}}\genfrac(){0.0pt}0{2n}{n}}$$ .