Type Ii Blow Up Manifolds For The Energy Supercritical Semilinear Wave Equation

Author : Charles Collot
Publisher : American Mathematical Soc.
Page : 163 pages
File Size : 42,5 Mb
Release : 2018-03-19
Category : Manifolds (Mathematics)
ISBN : 9781470428136

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Type II Blow Up Manifolds for the Energy Supercritical Semilinear Wave Equation by Charles Collot Pdf

Our analysis adapts the robust energy method developed for the study of energy critical bubbles by Merle-Rapha¨el-Rodnianski, Rapha¨el-Rodnianski and Rapha¨el- Schweyer, the study of this issue for the supercritical semilinear heat equation done by Herrero-Vel´azquez, Matano-Merle and Mizoguchi, and the analogous result for the energy supercritical Schr¨odinger equation by Merle-Rapha¨el-Rodnianski.

Author : Charles Collot,Pierre Raphaël,Jeremie Szeftel
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 55,9 Mb
Release : 2019-09-05
Category : Electronic
ISBN : 9781470436261

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On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation by Charles Collot,Pierre Raphaël,Jeremie Szeftel Pdf

The authors consider the energy super critical semilinear heat equation The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

Author : Maxwell Stolarski
Publisher : American Mathematical Society
Page : 160 pages
File Size : 49,7 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470468767

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Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow by Maxwell Stolarski Pdf

View the abstract.

Author : Michael Aschbacher
Publisher : American Mathematical Soc.
Page : 182 pages
File Size : 42,5 Mb
Release : 2019-02-21
Category : Electronic
ISBN : 9781470435202

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On Fusion Systems of Component Type by Michael Aschbacher Pdf

This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups. Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.

Author : Andreas Seeger,Charles K. Smart,Brian Street
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 50,9 Mb
Release : 2019-02-21
Category : Forms (Mathematics)
ISBN : 9781470434373

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Multilinear Singular Integral Forms of Christ-Journé Type by Andreas Seeger,Charles K. Smart,Brian Street Pdf

Author : Nawaf Bou-Rabee,Eric Vanden-Eijnden
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 53,9 Mb
Release : 2019-01-08
Category : Random walks (Mathematics)
ISBN : 9781470431815

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Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations by Nawaf Bou-Rabee,Eric Vanden-Eijnden Pdf

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.

Author : Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 44,9 Mb
Release : 2018-10-03
Category : Bounded mean oscillation
ISBN : 9781470429546

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Bellman Function for Extremal Problems in BMO II: Evolution by Paata Ivanisvili,Dmitriy M. Stolyarov,Vasily I. Vasyunin,Pavel B. Zatitskiy Pdf

In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.

Author : Sergey Fomin,Professor Dylan Thurston
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 55,8 Mb
Release : 2018-10-03
Category : Cluster algebras
ISBN : 9781470429676

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Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths by Sergey Fomin,Professor Dylan Thurston Pdf

For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.

Author : Joan Bosa,Nathanial P. Brown,Yasuhiko Sato,Aaron Tikuisis,Stuart White,Wilhelm Winter
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 44,9 Mb
Release : 2019-02-21
Category : C*-algebras
ISBN : 9781470434700

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Covering Dimension of C*-Algebras and 2-Coloured Classification by Joan Bosa,Nathanial P. Brown,Yasuhiko Sato,Aaron Tikuisis,Stuart White,Wilhelm Winter Pdf

The authors introduce the concept of finitely coloured equivalence for unital -homomorphisms between -algebras, for which unitary equivalence is the -coloured case. They use this notion to classify -homomorphisms from separable, unital, nuclear -algebras into ultrapowers of simple, unital, nuclear, -stable -algebras with compact extremal trace space up to -coloured equivalence by their behaviour on traces; this is based on a -coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, -stable -algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a “homotopy equivalence implies isomorphism” result for large classes of -algebras with finite nuclear dimension.

Author : Paul Feehan,Thomas G. Leness
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 49,8 Mb
Release : 2019-01-08
Category : Cobordism theory
ISBN : 9781470414214

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An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants by Paul Feehan,Thomas G. Leness Pdf

The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.

Author : Oliver Lorscheid,Thorsten Weist
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 54,7 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436476

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Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces by Oliver Lorscheid,Thorsten Weist Pdf

Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.

Author : T. Alazard,N. Burq,C. Zuily
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 44,5 Mb
Release : 2019-01-08
Category : Cauchy problem
ISBN : 9781470432034

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Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations by T. Alazard,N. Burq,C. Zuily Pdf

This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

Author : Werner Hoffmann,Satoshi Wakatsuki
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 47,7 Mb
Release : 2018-10-03
Category : Electronic
ISBN : 9781470431020

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On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 by Werner Hoffmann,Satoshi Wakatsuki Pdf

The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.

Author : Atanas Atanasov,Eric Larson,David Yang
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 54,5 Mb
Release : 2019-02-21
Category : Curves, Algebraic
ISBN : 9781470434892

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Interpolation for Normal Bundles of General Curves by Atanas Atanasov,Eric Larson,David Yang Pdf

Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.

Author : Alexandru D. Ionescu,Fabio Pusateri
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 46,6 Mb
Release : 2019-01-08
Category : Capillarity
ISBN : 9781470431037

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Global Regularity for 2D Water Waves with Surface Tension by Alexandru D. Ionescu,Fabio Pusateri Pdf

The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.