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## Regularity and Blow up for Active Scalars

Math. Model. Nat. Phenom., 5 4 (2010) 225-255
Published online: 2010-05-12

## Weak-strong uniqueness criterion for the $$\beta$$ β -generalized surface quasi-geostrophic equation

Jihong Zhao and Qiao Liu
Monatshefte für Mathematik 172 (3-4) 431 (2013)
DOI: 10.1007/s00605-013-0521-2

## On the global regularity of generalized Leray-alpha type models

Kazuo Yamazaki
Nonlinear Analysis: Theory, Methods & Applications 75 (2) 503 (2012)
DOI: 10.1016/j.na.2011.08.051

## Global well-posedness of the transport equation with nonlocal velocity in Besov spaces with critical and supercritical dissipation

Kazuo Yamazaki
Nonlinearity 24 (7) 2047 (2011)

## Hölder continuity for a drift-diffusion equation with pressure

Luis Silvestre and Vlad Vicol
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 29 (4) 637 (2012)
DOI: 10.1016/j.anihpc.2012.02.003

## On the regularity criteria of a surface quasi-geostrophic equation

Kazuo Yamazaki
Nonlinear Analysis: Theory, Methods & Applications 75 (13) 4950 (2012)
DOI: 10.1016/j.na.2012.04.010

## Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations

Peter Constantin, Nathan Glatt-Holtz and Vlad Vicol
Communications in Mathematical Physics 330 (2) 819 (2014)
DOI: 10.1007/s00220-014-2003-3

## Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations

Dongho Chae, Peter Constantin and Jiahong Wu
Archive for Rational Mechanics and Analysis 202 (1) 35 (2011)
DOI: 10.1007/s00205-011-0411-5

## Bifurcating steady-state solutions of the dissipative quasi-geostrophic equation in Lagrangian formulation

Zhi-Min Chen
Nonlinearity 29 (10) 3132 (2016)
DOI: 10.1088/0951-7715/29/10/3132

## On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion

Omar Lazar
Journal of Differential Equations 261 (9) 4974 (2016)
DOI: 10.1016/j.jde.2016.07.009

## Global well-posedness for a modified critical dissipative quasi-geostrophic equation

Changxing Miao and Liutang Xue
Journal of Differential Equations 252 (1) 792 (2012)
DOI: 10.1016/j.jde.2011.08.018

## Maximum palinstrophy growth in 2D incompressible flows

Diego Ayala and Bartosz Protas
Journal of Fluid Mechanics 742 340 (2014)
DOI: 10.1017/jfm.2013.685

## On a multi-dimensional transport equation with nonlocal velocity

Hongjie Dong
Advances in Mathematics 264 747 (2014)
DOI: 10.1016/j.aim.2014.07.028

## On the Serrin’s regularity criterion for the β-generalized dissipative surface quasi-geostrophic equation

Jihong Zhao and Qiao Liu
Chinese Annals of Mathematics, Series B 36 (6) 947 (2015)
DOI: 10.1007/s11401-015-0932-6

## Global solutions for a supercritical drift–diffusion equation

Jan Burczak and Rafael Granero-Belinchón
Advances in Mathematics 295 334 (2016)
DOI: 10.1016/j.aim.2016.03.011

## Large-time behavior of periodic solutions to fractal Burgers equation with large initial data

Lijuan Wang and Weike Wang
Chinese Annals of Mathematics, Series B 33 (3) 405 (2012)
DOI: 10.1007/s11401-012-0710-7

## Inviscid Limits for Active Scalar Equations with Mildly Singular Gradients

Walter Rusin
Journal of Mathematical Fluid Mechanics 15 (2) 415 (2013)
DOI: 10.1007/s00021-012-0113-2

## On the Second Iterate for Critically Diffusive Active Scalar Equations

Susan Friedlander and Walter Rusin
Journal of Mathematical Fluid Mechanics 15 (3) 481 (2013)
DOI: 10.1007/s00021-012-0121-2

## Well-posedness of a 1D transport equation with nonlocal velocity in the Lei-Lin space

Yanghai Yu, Xing Wu and Yanbin Tang
Mathematical Methods in the Applied Sciences 40 (4) 947 (2017)
DOI: 10.1002/mma.4026

## Logarithmically extended global regularity result of Lans-alpha MHD system in two-dimensional space

Durga KC and Kazuo Yamazaki
Journal of Mathematical Analysis and Applications 425 (1) 234 (2015)
DOI: 10.1016/j.jmaa.2014.12.024

## Self-similar solutions for active scalar equations in Fourier–Besov–Morrey spaces

Lucas C. F. Ferreira and Lidiane S. M. Lima
Monatshefte für Mathematik 175 (4) 491 (2014)
DOI: 10.1007/s00605-014-0659-6

## Global well-posedness for the two-dimensional Muskat problem with slope less than 1

Stephen Cameron
Analysis & PDE 12 (4) 997 (2019)
DOI: 10.2140/apde.2019.12.997

## A family of dissipative active scalar equations with singular velocity and measure initial data

Lucas C.F. Ferreira
Computers & Mathematics with Applications 64 (10) 3292 (2012)
DOI: 10.1016/j.camwa.2012.01.074

## Note on the weak–strong uniqueness criterion for the β -QG in Morrey–Campanato space

Saddek Gala and Maria Alessandra Ragusa
Applied Mathematics and Computation 293 65 (2017)
DOI: 10.1016/j.amc.2016.08.011

## Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation

Terence Tao
Annals of PDE 2 (2) (2016)
DOI: 10.1007/s40818-016-0019-z

## A Remark on the Two-Dimensional Magneto-Hydrodynamics-Alpha System

Kazuo Yamazaki
Journal of Mathematical Fluid Mechanics 18 (3) 609 (2016)
DOI: 10.1007/s00021-016-0259-4

## Extreme vortex states and the growth of enstrophy in three-dimensional incompressible flows

Diego Ayala and Bartosz Protas
Journal of Fluid Mechanics 818 772 (2017)
DOI: 10.1017/jfm.2017.136

## Global regularity for the supercritical active scalars

Haifeng Shang, Yana Guo and Mengmeng Song
Zeitschrift für angewandte Mathematik und Physik 68 (3) (2017)
DOI: 10.1007/s00033-017-0810-z