-
作者：Coron, Jean-Michel; Lissy, Pierre
作者单位：Institut Universitaire de France; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：In this paper, we prove a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain of R-3 with null Dirichlet boundary conditions. The control is distributed in an arbitrarily small nonempty open subset and has two vanishing components. Lions and Zuazua proved that the linearized system is not necessarily null controllable even if the control is distributed on the entire domain, hence the standard linearization method fails. We use the re...
-
作者：Hersh, Patricia
作者单位：North Carolina State University
摘要：Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the question of Bernstein of identifying regular CW complexes arising naturally from representation theory having ...
-
作者：Ni, Lei
作者单位：University of California System; University of California San Diego
-
作者：Pasten, Hector; Pheidas, Thanases; Vidaux, Xavier
作者单位：Queens University - Canada; University of Crete; Universidad de Concepcion
摘要：We show that first order integer arithmetic is uniformly positive-existentially interpretable in large classes of (subrings of) function fields of positive characteristic over some languages that contain the language of rings. One of the main intermediate results is a positive existential definition (in these classes), uniform among all characteristics p, of the binary relation or for some integer sa parts per thousand yen0. A natural consequence of our work is that there is no algorithm to d...
-
作者：Fraczek, Krzysztof; Ulcigrai, Corinna
作者单位：Nicolaus Copernicus University; University of Bristol
摘要：We give a criterion which proves non-ergodicity for certain infinite periodic billiards and directional flows on -periodic translation surfaces. Our criterion applies in particular to a billiard in an infinite band with periodically spaced vertical barriers and to the Ehrenfest wind-tree model, which is a planar billiard with a -periodic array of rectangular obstacles. We prove that, in these two examples, both for a full measure set of parameters of the billiard tables and for tables with rat...
-
作者：Mayboroda, Svitlana; Maz'ya, Vladimir
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Liverpool; Linkoping University
摘要：The present paper establishes boundedness of derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of , 2a parts per thousand currency signna parts per thousand currency sign2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.
-
作者：Naud, Frederic
作者单位：Avignon Universite
摘要：Let X = Gamma\H-2 be a convex co-compact hyperbolic surface and let delta be the Hausdorff dimension of the limit set. Let Delta(X) be the hyperbolic Laplacian. We show that the density of resonances of the Laplacian Delta(X) in rectangles {sigma <= Re(s) <= delta, vertical bar Im(s)vertical bar <= T} is less than O(T1+tau(sigma)) in the limit T -> infinity, where tau(sigma) < delta as long as sigma > delta/2. This improves the previous fractal Weyl upper bound of Zworski (Invent. Math. 136(2)...
-
作者：Jossen, Peter
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that the statement analogous to the Mumford-Tate conjecture for Abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image of the absolute Galois group with the unipotent part of the motivic fundamental group.
-
作者：Gan, Wee Teck; Qiu, Yannan; Takeda, Shuichiro
作者单位：National University of Singapore; University of Missouri System; University of Missouri Columbia
摘要：In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis.
-
作者：Parimala, R.; Suresh, V.
作者单位：Emory University
摘要：Let K be a complete discretely valued field with residue field kappa and F the function field of a curve over K. Let p be the characteristic of kappa and a a prime not equal to p. If the Brauer a-dimensions of all finite extensions of kappa are bounded by d and the Brauer a-dimensions of all extensions of kappa of transcendence degree at most 1 are bounded by d+1, then it is known that the Brauer a-dimension of F is at most d+2 (Lieblich in J. Reine Angew. Math. 659:1-41, 2011; Saltman in J. R...
