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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
Asymptotic decomposition for semilinear Wave and equivariant wave map equations
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
Minimal L3-Initial Data for Potential Navier-Stokes Singularities
A simple proof of the existence of initial data with minimal $L^3$-norm for potential Navier--Stokes singularities, recently established in [I. Gallagher, G. Koch, and F. Planchon], based on techniques based on profile decomposition is given.
Soliton resolution along a sequence of times for the focusing energy critical wave equation
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
Inviscid Damping Near the Couette Flow in a Channel
  • A. Ionescu, H. Jia
  • Mathematics
    Communications 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
Nonlinear inviscid damping near monotonic shear flows
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
Universality of blow up profile for small blow up solutions to the energy critical wave map equation
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
Linear Inviscid Damping in Gevrey Spaces
  • H. Jia
  • Mathematics
    Archive 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
Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case
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