Nonuniqueness of weak solutions to the SQG equation

T Buckmaster, S Shkoller, V Vicol - Communications on Pure …, 2019‏ - Wiley Online Library
We prove that weak solutions of the inviscid SQG equations are not unique, thereby
answering Open Problem 11 of De Lellis and Székelyhidi in 2012. Moreover, we also show …

A data assimilation algorithm for the subcritical surface quasi-geostrophic equation

MS Jolly, VR Martinez, ES Titi - Advanced Nonlinear Studies, 2017‏ - degruyter.com
In this article, we prove that data assimilation by feedback nudging can be achieved for the
three-dimensional quasi-geostrophic equation in a simplified scenario using only large …

Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation

MS Jolly, VR Martinez, EJ Olson, ES Titi - Chinese Annals of Mathematics …, 2019‏ - Springer
An intrinsic property of almost any physical measuring device is that it makes observations
which are slightly blurred in time. The authors consider a nudging-based approach for data …

The Generalized Caffarelli‐Kohn‐Nirenberg Theorem for the Hyperdissipative Navier‐Stokes System

M Colombo, C De Lellis… - Communications on Pure …, 2020‏ - Wiley Online Library
The Generalized Caffarelliâ•’Kohnâ•’Nirenberg Theorem for the Hyperdissipative Navierâ•’Stokes
System Page 1 The Generalized Caffarelli-Kohn-Nirenberg Theorem for the Hyperdissipative …

[PDF][PDF] Regularity results for the 2D Boussinesq equations with critical or supercritical dissipation

J Wu, X Xu, L Xue, Z Ye - Communications in Mathematical …, 2016‏ - math0.bnu.edu.cn
The incompressible Boussinesq equations serve as an important model in geophysics as
well as in the study of Rayleigh–Bénard convection. One generalization is to replace the …

Global well-posedness for supercritical SQG with perturbations of radially symmetric data

A Bulut, H Dong - International Mathematics Research Notices, 2024‏ - academic.oup.com
We study the global well-posedness of the supercritical dissipative surface quasi-
geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well …

[HTML][HTML] Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation

T Iwabuchi - Annales de l'Institut Henri Poincaré C, Analyse non …, 2020‏ - Elsevier
This paper is concerned with the Cauchy problem of the Burgers equation with the critical
dissipation. The well-posedness and analyticity in both of the space and the time variables …

[HTML][HTML] Regularity results for a class of generalized surface quasi-geostrophic equations

O Lazar, L Xue - Journal de Mathématiques Pures et Appliquées, 2019‏ - Elsevier
We show a global existence result of weak solutions for a class of generalized Surface
Quasi-Geostrophic equation in the inviscid case. We also prove the global regularity of such …

On the Regularity of Solutions to Some Active Scalar Equations on Bounded Domains

E Abdo - SIAM Journal on Mathematical Analysis, 2024‏ - SIAM
We consider a family of fractionally dissipative active scalar equations (including the surface
quasi-geostrophic and incompressible porous media models) on two-dimensional bounded …

On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces

MS Jolly, A Kumar, VR Martinez - Communications in Mathematical …, 2021‏ - Springer
This paper studies the dissipative generalized surface quasi-geostrophic equations in a
supercritical regime where the order of the dissipation is small relative to order of the …