Date/Time : 11 Oct 2023 14:30
Venue : S17 #05-11 (SR5)
Speaker : Chen Shibing, University of Science and Technology of China

Optimal partial transportation is an important generalization of the classical optimal transport problem, and it arises in many applications, such as image retrieval. Mathematically, the problem was first studied by Caffarelli and McCann. They established the existence, uniqueness, and Holder regularity of the free normal and the map near the free boundary while leaving open the question of their higher regularity. In this talk, we will introduce our recent work in this direction.

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Date/Time : 04 Oct 2023 14:30
Venue : S17 #05-11 (SR5)
Speaker : Shiwu Yang, Peking University

It has been shown that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space decay like linear solutions. One hence can define the associated radiation field on the future null infinity. In this talk, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem to the MKG system with general large data by using gauge invariant vector field method. This is based on joint work with W. Dai, H. Mei and D. Wei.

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Date/Time : 17 Aug 2023 13:00
Venue : S17 #04-04 (SR3)
Speaker : Wang Fei, Shanghai Jiaotong University.

This paper concerns the existence of global weak solutions {\it \`a la Leray} for compressible Navier–Stokes–Fourier system with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

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Date/Time : 16 Aug 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Chengbo Wang, Zhejiang University

In this talk, I will present a sharp local well-posedness result for spherically symmetric solutions to quasilinear wave equations with rough initial data, when the spatial dimension is three or higher. Our approach is based on Morawetz type local energy estimates with fractional regularity for linear wave equations with variable C^1 coefficients, which rely on multiplier method, weighted Littlewood-Paley theory, duality and interpolation. Together with weighted linear and nonlinear estimates (including weighted trace estimates, Hardy’s inequality, fractional chain rule and fractional Leibniz rule) which are adapted for the problem, the well-posed result is proved by iteration. In addition, our argument yields almost global existence for n=3 and global existence for dimension 4 and higher, when the initial data are small, spherically symmetric with almost critical Sobolev regularity.

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Date/Time : 16 Aug 2023 16:10
Venue : S17 #04-04 (SR3)
Speaker : Naqing Xie, Fudan University

We discuss a uniqueness result of the electro-vacuum Einstein-Maxwell equations near the null infinity. This talk is based on a recent joint work with Xiaokai He (Hunan First Normal, Changsha) and Xiaoning Wu (AMSS, CAS, Beijing).

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Date/Time : 30 Jun 2023 22:00
Venue : via Zoom
Speaker : Dawei Shen, Sorbonne University

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https://nus-sg.zoom.us/j/83328843795?pwd=bUEvRU5UaVJad054UFUzV2RaUTZsQT09

Meeting ID: 833 2884 3795
Passcode: 706950

I will start with an introduction of the Einstein-vacuum equations and the history of stability problems of black holes. Then, I will talk about the double null foliations of spacetimes, which induce the null structure equations and Bianchi equations. Next, I will introduce the linearization procedure and the linearized equations. Finally, I will present my main result, which provides a new proof of Kerr stability in external regions, which was first obtained by Caciotta-Nicolò in 2010 using vectorfield method.

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Date/Time : 30 Mar 2022 16:00
Venue : via Zoom
Speaker : Zexing Li, University of Cambridge

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https://nus-sg.zoom.us/j/86113239460?pwd=anRLYzEvaGFQVGVLNVF3dGVRM1pOUT09

Meeting ID: 861 1323 9460
Passcode: 220330

Abstract: The Chern-Simons-Schr\”odinger equation is a nonrelativistic quantum model describing the dynamics of a large number of charged particles in the plane interacting both directly and via a self-generated electromagnetic field. Mathematically, it is a gauged $L^2$-critical Schr\”odinger equation has soliton behavior. Considering the equivariant and self-dual case, Liu-Smith has proved below threshold charge wellposedness via concentration compactness method. In this talk, I will present our result on characterizing dynamics at the threshold charge. This is a joint work with Baoping Liu.

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Date/Time : 20 Oct 2021 09:00
Venue : via Zoom
Speaker : Siqi He, Stony Brook University

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https://nus-sg.zoom.us/j/88336974987?pwd=SVVRVStaVTJ6STVEL1JGRSsxQjVFdz09

Meeting number：883 3697 4987
Password：132347

Abstract: Special Lagrangian submanifolds are a distinguished class of real calibrated submanifolds defined in a Calabi-Yau manifold, which are calibrated by the real part of the holomorphic volume form. Given a compact, smooth special Lagrangian submanifold, Mclean proved that the space of nearby special Lagrangian submanifolds of it could be parametrized by the harmonic 1-forms. In this talk, we will discuss some recent progress on generalizing Mclean’s result to the branched deformations. We will describe how to use multi-valued harmonic functions to construct branched nearby deformations.

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Date/Time : 26 May 2021 15:00
Venue : via Zoom
Speaker : Wen Deng, Chinese Academy of Sciences

Join Zoom Meeting https://nus-sg.zoom.us/j/83402872988?pwd=UWxhOEFKam9oYnk1N1FqT2JCdnFzdz09 Meeting ID: 834 0287 2988 Password: 471879 We consider the stability problem of the Couette flow for the 2D Boussinesq system. Due to the presence of the buoyancy forcing, the energy of the standard Boussinesq equations could grow in time. It is the enhanced dissipation created by the linear non self-adjoint operator in the perturbation equation that makes the stability possible. In this work, we prove the nonlinear stability of the Couette flow for 2D Boussinesq system with full dissipation and with only vertical dissipation in Sobolev spaces. This is a joint work with J. Wu and P. Zhang.

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