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In this talk, we consider the incompressible Navier-Stokes equations with free boundary, which has a finite-time splash singularity for a large class of specially prepared initial data. The approach i...
In this talk, I first discuss isometric embedding from differential geometry and its relation with fluid mechanic equations. Then I will present recent progress and my works on isometric embeddings of...
疏散波(rarefaction wave)、激波(shock wave)和涡片波(vortex sheet)是可压缩流体中的三类基本波形,它们分别对应可压缩流体的疏散、压缩和剪切三类不同的物理现象。本次报告将研究对于可压缩Navier-Stokes方程,即考虑流体的粘性效应时,这三类波现象在小扰动下的稳定性。特别地,这里的扰动在空间无穷远处可以周期振荡,这类非局部扰动不仅带来数学上的新困难,也让我...
We are motivated to study this problem so that the proof of Arnold Diffusion of many degrees of freedom can be significantly simplified.
In this talk, we consider the long-time behavior of the linearized MHD equations around a steady flowing plasma. We confirm the following physical phenomenon: there will be a generation of a magnetic ...
相变与临界现象是最引人注目的物理现象之一。在连续相变点附近,许多看似截然不同的物理体系具有不依赖于微观细节的性质—即普适性。在临界点附近,处于同一普适类的物理系统的物理量随着体系参数的变化表现出普适的标度律。
由于油气资源的成分复杂,油藏工程师在描述原油的性质时,常常需要使用不同的数学模型。除了经典的黑油模型之外,还有诸如热采模型、裂缝模型、多重介质模型等。一些提高采收率技术通常基于更一般的组分模型框架来进行数值模拟,例如聚合物驱油剂、表面活化剂驱油剂、碱驱油剂、微生物驱油剂、低盐度水驱等。此外,二氧化碳埋藏、地下水污染治理、地热资源开采等应用问题也可使用组分模型来模拟。这些重要的应用使得多相多组分模拟...
In this talk, I will discuss the method of convex integration and its applications on non-uniqueness of weak solutions to the hyper-viscous incompressible Navier-Stokes equations as well as the hypo-v...
We investigate the convergence rate in the vanishing viscosity process of the solutions to the subquadratic state-constraint Hamilton-Jacobi equations. We give two different proofs of the fact that, f...
In this talk, we will first go over the history of Schauder estimates, where the developing of proofs will be emphasized. Second, we will establish pointwise interior Schauder estimates for Stokes sys...
A smooth projective variety X is called rigid if any deformation of X is isomorphic to itself. A first example is the projective space, but in general it is a subtle and difficult problem to prove the...
有机硅改性涂层具有优异的低表面能自润滑特性,可有效减少水滴在涂层表面的附着,一定程度上能延缓积冰的形成,降低覆冰强度。

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