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European Mathematical Society Publishing House
2024-03-29 10:51:45
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=34&iss=3&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
34
1998
3
On the Hydrodynamic Limit of the Enskog Equation
Miroslaw
Lachowicz
University of Warsaw, WARSAW, POLAND
Enskog equation, Euler system, singularly perturbed problem, hydrodynamie limit
The Enskog equation in the hydrodynamie limit is investigated. If the Knudsen number ε and the scale of diameter a of the hard sphere particles are of the same order, the resulting system of hydrodynamie equations (the Enskog-Euler system) is different from that for the Boltzmann equation. The existence and uniqueness theorem, in this case for the Enskog equation, is proven on the time interval independent of the small parameters. As ε ↓ 0, the solution of the Enskog equation tends to the Maxwellian whose fluid-dynamic parameters solve the Enskog-Euler system. As a by-product — the existence theorem for the Enskog-Euler system is obtained.
Statistical mechanics, structure of matter
General
191
210
10.2977/prims/1195144692
http://www.ems-ph.org/doi/10.2977/prims/1195144692
Spherically Symmetric Dirac Operators with Variable Mass and Potentials Infinite at Infinity
Karl Michael
Schmidt
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
Osanobu
Yamada
Kyoto University, KYOTO, JAPAN
Enskog equation, Euler system, singularly perturbed problem, hydrodynamie limit
We study the spectrum of spherically symmetric Dirac operators m three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete: we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.
Quantum theory
General
211
227
10.2977/prims/1195144693
http://www.ems-ph.org/doi/10.2977/prims/1195144693
Standard Monomial Theory for Bott-Samelson Varieties of GL (n)
Venkatramani
Lakshmibai
Northeastern University, BOSTON, UNITED STATES
Peter
Magyar
Michigan State University, EAST LANSING, UNITED STATES
Enskog equation, Euler system, singularly perturbed problem, hydrodynamie limit
We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Zi associated to G= GL (n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties.
Algebraic geometry
General
229
248
10.2977/prims/1195144694
http://www.ems-ph.org/doi/10.2977/prims/1195144694
Gevrey Wellposedness of the Cauchy Problem for the Hyperbolic Equations of Third Order with Coefficients Depending Only on Time
Tamotu
Kinoshita
University of Tsukuba, IBARAKI, JAPAN
We shall show the Gevrey wellposedness of the Cauchy problem for the hyperbolic equations of third order with coefficients depending only on time. For the proof we use the suitable energy of the third order equations.
Partial differential equations
General
249
270
10.2977/prims/1195144695
http://www.ems-ph.org/doi/10.2977/prims/1195144695
Equivariant Maps between Representation Spheres of a Torus
Katsuhiro
Komiya
Yamaguchi University, YAMAGUCHI CITY, JAPAN
Algebraic topology
General
271
276
10.2977/prims/1195144696
http://www.ems-ph.org/doi/10.2977/prims/1195144696
On a Solution of a q-Difference Analogue of Laurieella's D-Type Hypergeometric Equation with |q| = 1
Michitomo
Nishizawa
Waseda University, TOKYO, JAPAN
By using the double sine function, an integral solution of a q-difference analogue of Laurieella's D-type hypergeometric equation is constructed in the case when |q| = 1. Furthermore, its contiguity operators are considered.
Algebraic topology
General
277
290
10.2977/prims/1195144697
http://www.ems-ph.org/doi/10.2977/prims/1195144697