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## Regularity and Blow up for Active Scalars

Math. Model. Nat. Phenom., 5 4 (2010) 225-255

## 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)

## 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

## Remarks on a nonlocal transport

Dong Li and Jose Rodrigo
Advances in Mathematics 374 107345 (2020)
DOI: 10.1016/j.aim.2020.107345

## 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

## Selection of singular solutions in non-local transport equations

J Eggers and M A Fontelos
Nonlinearity 33 (1) 325 (2020)
DOI: 10.1088/1361-6544/ab4e0b

## 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

## 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 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

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

Annales de l'Institut Henri Poincaré C, Analyse non linéaire 29 (4) 637 (2012)
DOI: 10.1016/j.anihpc.2012.02.003

## On the Effects of Advection and Vortex Stretching

Tarek M. Elgindi and In-Jee Jeong
Archive for Rational Mechanics and Analysis 235 (3) 1763 (2020)
DOI: 10.1007/s00205-019-01455-9

## Global smoothness for a 1D supercritical transport model with nonlocal velocity

Lucas Ferreira and Valter Moitinho
Proceedings of the American Mathematical Society 148 (7) 2981 (2020)
DOI: 10.1090/proc/14984

## The Burgers’ equation with stochastic transport: shock formation, local and global existence of smooth solutions

Diego Alonso-Orán, Aythami Bethencourt de León and So Takao
Nonlinear Differential Equations and Applications NoDEA 26 (6) (2019)
DOI: 10.1007/s00030-019-0602-6

## Global existence for some transport equations with nonlocal velocity

Hantaek Bae and Rafael Granero-Belinchón
Advances in Mathematics 269 197 (2015)
DOI: 10.1016/j.aim.2014.10.016

## 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

## 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

## Bounded mean oscillation and the uniqueness of active scalar equations

Jonas Azzam and Jacob Bedrossian
Transactions of the American Mathematical Society 367 (5) 3095 (2014)
DOI: 10.1090/S0002-9947-2014-06040-6

## Fractional Stochastic Active Scalar Equations Generalizing the Multi-Dimensional Quasi-Geostrophic & 2D-Navier–Stokes Equations: The General Case

Latifa Debbi
Journal of Mathematical Fluid Mechanics 22 (4) (2020)
DOI: 10.1007/s00021-020-00509-3

## Singularity formation and global Well-posedness for the generalized Constantin–Lax–Majda equation with dissipation

Jiajie Chen
Nonlinearity 33 (5) 2502 (2020)
DOI: 10.1088/1361-6544/ab74b0

## Maximum amplification of enstrophy in three-dimensional Navier–Stokes flows

Di Kang, Dongfang Yun and Bartosz Protas
Journal of Fluid Mechanics 893 (2020)
DOI: 10.1017/jfm.2020.204

## 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

## Long time localization of modified surface quasi-geostrophic equations

Guido Cavallaro, Roberto Garra and Carlo Marchioro
Discrete & Continuous Dynamical Systems - B 26 (9) 5135 (2021)
DOI: 10.3934/dcdsb.2020336

## Stable self-similar blow-up for a family of nonlocal transport equations

Tarek M. Elgindi, Tej-eddine Ghoul and Nader Masmoudi
Analysis & PDE 14 (3) 891 (2021)
DOI: 10.2140/apde.2021.14.891

## On the global well-posedness of one-dimensional fluid models with nonlocal velocity

Zhuan Ye
Pacific Journal of Mathematics 304 (2) 713 (2020)
DOI: 10.2140/pjm.2020.304.713

## The incompressible Euler equations under octahedral symmetry: Singularity formation in a fundamental domain

Tarek M. Elgindi and In-Jee Jeong
Advances in Mathematics 393 108091 (2021)
DOI: 10.1016/j.aim.2021.108091

## Ergodicity of Galerkin approximations of surface quasi-geostrophic equations and Hall-magnetohydrodynamics system forced by degenerate noise

Kazuo Yamazaki
Nonlinear Differential Equations and Applications NoDEA 29 (2) (2022)
DOI: 10.1007/s00030-022-00753-8

## Formation of singularities for multi-dimensional transport equations with nonlocal velocity

Quansen Jiu and Wanwan Zhang
Journal d'Analyse Mathématique 146 (1) 385 (2022)
DOI: 10.1007/s11854-022-0197-4

## Global existence, blow-up and stability for a stochastic transport equation with non-local velocity

Diego Alonso-Orán, Yingting Miao and Hao Tang
Journal of Differential Equations 335 244 (2022)
DOI: 10.1016/j.jde.2022.06.025

## Searching for Singularities in Navier–Stokes Flows Based on the Ladyzhenskaya–Prodi–Serrin Conditions

Di Kang and Bartosz Protas
Journal of Nonlinear Science 32 (6) (2022)
DOI: 10.1007/s00332-022-09832-7

## On the blow up of a non-local transport equation in compact manifolds

Diego Alonso-Orán and Ángel Martínez
Proceedings of the American Mathematical Society (2022)
DOI: 10.1090/proc/16138

## The Speed of Traveling Waves in a FKPP-Burgers System

Jason J. Bramburger and Christopher Henderson
Archive for Rational Mechanics and Analysis 241 (2) 643 (2021)
DOI: 10.1007/s00205-021-01660-5

## Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations

Jiajie Chen, Thomas Y. Hou and De Huang
Annals of PDE 8 (2) (2022)
DOI: 10.1007/s40818-022-00140-7