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Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (−1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive… Expand

Asymptotic decomposition for semilinear Wave and equivariant wave map equations

- H. Jia, Hao Carlos Kenig
- Mathematics
- 23 March 2015

abstract:In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two… Expand

Minimal L3-Initial Data for Potential Navier-Stokes Singularities

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Soliton resolution along a sequence of times for the focusing energy critical wave equation

- Thomas Duyckaerts, H. Jia, C. Kenig, F. Merle
- Mathematics
- 8 January 2016

In this paper, we prove that any solution of the energy-critical wave equation in space dimensions 3, 4 or 5, which is bounded in the energy space decouples asymptotically, for a sequence of times… Expand

Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?

- H. Jia, Vladim'ir vSver'ak
- Mathematics
- 10 June 2013

Inviscid Damping Near the Couette Flow in a Channel

- A. Ionescu, H. Jia
- MathematicsCommunications in Mathematical Physics
- 13 August 2018

We prove asymptotic stability of the Couette flow for the 2D Euler equations in the domain $$\mathbb {T}\times [0,1]$$ T × [ 0 , 1 ] . More precisely we prove that if we start with a small and smooth… Expand

Nonlinear inviscid damping near monotonic shear flows

- A. Ionescu, H. Jia
- Mathematics
- 9 January 2020

We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear… Expand

Universality of blow up profile for small blow up solutions to the energy critical wave map equation

- Thomas Duyckaerts, H. Jia, C. Kenig, F. Merle
- Mathematics
- 15 December 2016

In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality for small energy wave… Expand

Linear Inviscid Damping in Gevrey Spaces

- H. Jia
- MathematicsArchive for Rational Mechanics and Analysis
- 2 April 2019

We prove linear inviscid damping near a general class of monotone shear flows in a finite channel, in Gevrey spaces. This is an essential step towards proving nonlinear inviscid damping for general… Expand

Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case

- H. Jia, Bao-ying Liu, W. Schlag, Guixiang Xu
- Mathematics
- 15 June 2015

In this paper, we continue our study [16] on the long time dynamics of radial solutions to defocusing energy critical wave equation with a trapping radial potential in 3 + 1 dimensions. For generic… Expand

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