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More on super-replication formulae
We extend Norton-Borcherds-Koike's replication formulae to super-replicable
ones by working with the congruence groups and find the product
identities which characterize super-replicable functions. These will provide a
clue for constructing certain new infinite dimensional Lie superalgebras whose
denominator identities coincide with the above product identities. Therefore it
could be one way to find a connection between modular functions and infinite
dimensional Lie algebras.Comment: 28 page
Global existence of non-Newtonian incompressible fluids in half space with nonhomogeneous initial-boundary data
In this study, we investigate the global existence of non-Newtonian
incompressible fluid governed by (1.1). We find the weak solutions for the
equations (1.1) in anisotropic Besov spaces . % with
nonhomogeneous boundary data. We also show that the solution is in . Furthermore, the
solutions are contained in . For the global existence of solutions, we assume that the
extra stress tensor is represented by , where is uniformly elliptic matrix
and \begin{align*} |\big( {\mathbb F}({\mathbb A}) -{\mathbb F}(0) \big)
{\mathbb A} - \big( {\mathbb F}({\mathbb B})- {\mathbb F}(0) \big){\mathbb B}|
\leq o(\max ( |{\mathbb A}|, |{\mathbb B}|) ) |{\mathbb A} -{\mathbb B}| \quad
\mbox{at zero}. \end{align*} Note that , and introduced in
(1.3) satisfy our assumption
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