×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.
Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

Transition threshold for the 2-D Couette flow in whole space via Green's function

Click here to flash read.

arXiv:2404.11878v1 Announce Type: new
Abstract: In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the linearized equations around Couette flow, we initially establish refined dissipation estimates for the linearized Navier-Stokes equations with a precise decay rate $(1+t)^{-1}.$ As an application, we prove that if the initial perturbation of vorticity satisfies$$\|\omega_{0}\|_{H^{1}\cap L^1}\leq c_0\nu^{\frac{3}{4}}$$ for some small constant $c_0$ independent of the viscosity $\nu$, then we can reach the conclusion that the solution remains within $O\left( \nu ^{\frac{3}{4}}\right) $ of the Couette flow.

Click here to read this post out
ID: 813164; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: April 19, 2024, 7:32 a.m. Changes:
/u/anonymous
Dictionaries:
Words:
Spaces:
Views: 8
CC:
No creative common's license
Comments: