Shuanglin shao
On the extremizers of an adjoint Fourier restriction inequality. Michael Christ, Shuanglin Shao. The adjoint Fourier restriction inequality for the sphere states that if then $\widehat {f\sigma}\in L^4 (\reals^3)$. We prove that all critical points of the functional $\norm {\widehat {f\sigma}}_ {L^4}/\norm {f}_ {\lt}$ are smooth; that any ...Shuanglin Shao. Mathematics. 2007; For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear ...Shuanglin Shao. We prove that the extremizers to the Tomas-Stein inequality for the one dimension sphere are smooth. This is achieved by studying the associated Euler-Lagrange equation. Comments: 11 pages. We rewrite some of the introduction part and correct Lemma 3.2 and proposition 3.6.
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Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: MF: 10:00 -- 11:00 AM, or by appointment. Miscellaneous There will be a take-home final in …Authors: Shuanglin Shao. Download PDF Abstract: In this paper, for cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and linear adjoint restriction estimates.Shuanglin Shao, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case, Rev. Mat. Iberoam. 25 (2009), no. 3, 1127–1168. MR 2590695, DOI 10.4171/RMI/591; Shuanglin Shao, A note on the cone restriction conjecture in the cylindrically symmetric case, Proc. Amer. Math. Soc. 137 (2009), no. 1, 135–143.Shuanglin Shao; In this paper, we establish the linear profile decomposition for the one-dimensional fourth order Schrödinger equation where μ⩾0. As an application, we establish a dichotomy ...SOONSIK KWON, SHUANGLIN SHAO Abstract. We consider the global dynamics of the defocusing generalized KdV equation @tu + @3 xu = @x(jujp 1u): We use Tao’s theorem [5] that the energy moves faster than the mass to prove a moment type dispersion estimate. As an application of the dispersion esti-From: Shuanglin Shao Mon, 8 Oct 2007 05:42:33 UTC (11 KB) [v2] Fri, 20 Jun 2008 05:30:27 UTC (9 KB) Full-text links: Download: Download a PDF of the paper titled A note on the cone restriction conjecture in the cylindrically symmetric case, by Shuanglin Shao. PDF; PostScript; Other formats Current browse context: ...Instructor: Shuanglin Shao Office: Snow Hall 615 Email: [email protected] Office Hour: M, W: 9:30-10:30 AM or by appointment. Grade Policy. 4 ene 2021 ... Title:A remark on the Strichartz inequality in one dimension. Authors:Ryan Frier, Shuanglin Shao. Download a PDF of the paper titled A remark ...The University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression, and genetic information in the university's programs and activities.JIN-CHENG JIANG AND SHUANGLIN SHAO Abstract. In this paper, we study the extremal problem for the Strichartz inequality for the Schr ̈ odinger equation on the R×R2. We …Shuanglin Shao. Mathematics. 2010; In [5], when the spatial variable x is localized, Lee observed that the Schrödinger maximal operator eit∆f(x) enjoys certain localization property in t for frequency localized functions. In this … Expand. Highly Influenced. PDF. 9 …Aug 31, 2008 · Download a PDF of the paper titled Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation, by Shuanglin Shao Download PDF Abstract: In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions ... Shuanglin Shao: 306 Snow: Thursday, 9/1/22: 4:00 pm: Graduate Student Probability Seminar Random Walk: A Modern Introduction Ray Zhang: 564 Snow: Friday, 9/2/22: 12:00 pm: GSO Seminar Intro to D-modules Christopher Wong: 256 Snow 3:00 pm: Combinatorics Seminar Counting Embeddings of Graphs in State Space Vance Gaffar, Baker University: 306 SnowAug 31, 2008 · Download a PDF of the paper titled Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation, by Shuanglin Shao Download PDF Abstract: In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions ... SHUANGLIN SHAO (Communicated by Hart F. Smith) Abstract. In this paper, we present two arguments showing that the classi-cal linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the ...
Shuanglin Shao Affiliation Mathematics Field of Study Analysis From 9/2008 – 8/2009 Shuanglin Shao works in harmonic analysis and partial differential equations. He is interested in establishing the profile decomposition result for the Airy equation, and the problem of pointwise convergence of solutions to the Schrödinger equation. Dates at IAS Download a PDF of the paper titled A remark on the two dimensional water wave problem with surface tension, by Shuanglin Shao and Hsi-Wei Shih. Download PDF Abstract: We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension ...Shao showed that when (α,d) = (2,2), then extremizers must be analytic, and used the functional equations in Foschi’s paper [10] to give an alternative proof to show that extremizers are Guassians. The second author and Shao showed that extremizers must be Gaussians for the case when (α,d) = (2,1) in [11] as well. Dec 9, 2022 · Shuanglin Shao: 306 Snow: Thursday, 9/1/22: 4:00 pm: Graduate Student Probability Seminar Random Walk: A Modern Introduction Ray Zhang: 564 Snow: Friday, 9/2/22: 12:00 pm: GSO Seminar Intro to D-modules Christopher Wong: 256 Snow 3:00 pm: Combinatorics Seminar Counting Embeddings of Graphs in State Space Vance Gaffar, Baker University: 306 Snow
SHUANGLIN SHAO AND HSI-WEI SHIH Abstract. We consider the motion of a two-dimensional interface be-tween air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into an equivalent quasilinear sys-Cite this article. Shuanglin Shao, Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case.Rev. Mat. Iberoam. 25 (2009), no. 3, pp. 1127–1168Shuanglin Shao Atanas Stefenov Date defended: May 11, 2015. The Dissertation Committee for Lucas Chaffee certifies that this is the approved version of the following dissertation : Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication Rodolfo Torres, Chairperson…
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In this thesis we are mainly concerned with local wellposedness (LWP) problems for nonlinear evolution equations, two global results will then be a direct consequence of conservation laws. A standard scheme to prove LWP is the application of the contraction mapping principle to the corresponding integral equation in a suitable …STATE OF NEW HAMPSHIRE CHAIRMAN Martin P. Königsberg TDD Access: Relay NH 18007352964 COMMISSIONERS Robert R. Scott Tel. (603)2712431 FAX No. 2713878 EXECUTIVE DIRECTOR Debra A. Howland Website:
Shuanglin Shao works in harmonic analysis and partia SHUANGLIN SHAO AND HSI-WEI SHIH Abstract. We consider the motion of a two-dimensional interface be-tween air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into an equivalent quasilinear sys- The first deals with multilinear determinant funcInstructor: Shuanglin Shao Office: Snow Hall 615 Shuanglin Shao is a professor in the Mathematics department at University of Kansas - see what their students are saying about them or leave a rating yourself.Posted by: Shuanglin Shao | August 15, 2020 Lecture 1 This semester we will study the measure theory and integration theory, namely Chapters 1,2,3, and 6 in … Shuanglin Shao (University of Kansas) On smoothness of Shuanglin Shao (KU) Department of Mathematics. 138 Cardwell Hall. 1228 N Martin Luther King Jr Drive, Manhattan, KS 66506 . 785-532-6750 | 785-532-0546 fax | math ... Posted by: Shuanglin Shao | August 15, 2020 Math 810: measure theory and integration. Lecture 1. This semester we will study the measure theory and integration theory, namely Chapters 1,2,3, and 6 in Folland’s real analysis book. The development of measure theory has a long history starting with Weierstrass’s construction of a nowhere ... Shao showed that when (α,d) = (2,2), then extremizers mu10 oct 2015 ... Shuanglin Shao's user avatar. SWe identify the compactness threshold for optimizing sequences of the Shuanglin Shao We prove that the extremizers to the Tomas-Stein inequality for the one dimension sphere are smooth. This is achieved by studying the associated Euler-Lagrange equation. Shuanglin was born in May 1, 1964 Shuanglin has Shuanglin Shao. Shuanglin Shao. Associate Professor. Contact Info. [email protected] · 785-864-4762. 627 Snow. Personal Links. Webpage Webpage. Research —.Aug 31, 2008 · Download a PDF of the paper titled Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schr\"odinger equation, by Shuanglin Shao Download PDF Abstract: In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions ... [30] Shao, Xiaolu, Li, Shuanglin, Liu, Na, Song, Jie. The[The adjoint Fourier restriction inequality of Tomas and SteiForbes China launched its first annual list to honor 50 T SHUANGLIN SHAO Abstract. In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr¨odinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schr¨oindger