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Vol 210, No 5 (2019)
- Year: 2019
- Articles: 4
- URL: https://journals.rcsi.science/0368-8666/issue/view/7453
Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$
Abstract
This paper is concerned with the topology of the Liouville foliation in the analogue of the Kovalevskaya integrable case on the Lie algebra $\operatorname{so}(4)$. The Fomenko-Zieschang invariants (that is, marked molecules) for this foliation are calculated on each nonsingular iso-energy surface. A detailed description of the resulting stratification of the three-dimensional space of parameters of the iso-energy surfaces is given. Bibliography: 23 titles.
Matematicheskii Sbornik. 2019;210(5):3-40
3-40
Besov classes on finite and infinite dimensional spaces
Abstract
We give an equivalent description of Besov spaces in terms of a new modulus of continuity. Then we use a similar approach to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure. Bibliography: 25 titles.
Matematicheskii Sbornik. 2019;210(5):41-71
41-71
Time decay estimates for solutions of the Cauchy problem for the modified Kawahara equation
Abstract
The large-time behaviour of solutions of the Cauchy problem for the modified Kawahara equation $$\begin{cases}u_t-\partial_xu^3-\frac a3\partial_x^3u+\frac b5\partial_x^5u=0,&(t,x)\in\mathbb R^2,u(0,x)=u_0(x),&x\in\mathbb R,\end{cases}$$where $a,b>0$, is investigated. Under the assumptions that the total mass of the initial data $\int u_0(x) dx$ is nonzero and the initial data $u_0$ are small in the norm of $\mathbf H^{2,1}$ it is proved that a global-in-time solution exists and estimates for its large-time decay are found. Bibliography: 19 titles.
Matematicheskii Sbornik. 2019;210(5):72-108
72-108
Admissible pairs vs Gieseker-Maruyama
Abstract
Morphisms between the moduli functor of admissible semistable pairs and the Gieseker-Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface are constructed. It is shown that these functors are isomorphic, and the moduli scheme for semistable admissible pairs $((\widetilde S,\widetilde L),\widetilde E)$ is isomorphic to the Gieseker-Maruyama moduli scheme. All the components of moduli functors and corresponding moduli schemes which exist are looked at here. Bibliography: 16 titles.
Matematicheskii Sbornik. 2019;210(5):109-134
109-134