| [1] |
Constantin P, Majda A J, Tabak E. Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar. Nonlinearity, 1994, 7(6): 1495-1533
doi: 10.1088/0951-7715/7/6/001
|
| [2] |
Held I M, Pierrehumbert R T, Garner S T, Swanson K L. Surface quasi-geostrophic dynamics. J Fluid Mech, 1995, 282: 1-20
doi: 10.1017/S0022112095000012
|
| [3] |
Lapeyre G. Surface quasi-geostrophy. Fluids, 2017, 2(1): 7
doi: 10.3390/fluids2010007
|
| [4] |
Majda A J, Bertozzi A L. Vorticity and Incompressible Flow. Cambridge: Cambridge UP, 2002
|
| [5] |
Castro A, Córdoba D, Gómez-Serrano J. Global Smooth Solutions for the Inviscid SQG Equation. Providence, RI: Amer Math Soc, 2020
|
| [6] |
Kiselev A, Ryzhik L, Yao Y, Zlato A. Finite time singularity for the modified SQG patch equation. Ann Math, 2016, 184: 909-948
doi: 10.4007/annals.2016.184-3
|
| [7] |
Gravejat P, Smets D. Smooth travelling-wave solutions to the inviscid surface quasigeostrophic equation. Int Math Res Not, 2019, 6: 1744-1757
|
| [8] |
Godard-Cadillac L. Smooth traveling-wave solutions to the inviscid surface quasi-geostrophic equations. C R Math Acad Sci Paris, 2021, 359: 85-98
|
| [9] |
Ao W, Dávila J, Pino L D, et al. Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation. Trans Amer Math Soc, 2021, 374(9): 6665-6689
doi: 10.1090/tran/2021-374-09
|
| [10] |
Castro A, Córdoba D, Gómez-Serraon J. Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations. Duke Math J, 2016, 165(5): 935-984
|
| [11] |
Hassainia Z, Hmidi T. On the V-states for the generalized quasi-geostrophic equations. Commun Math Phys, 2015, 337(1): 321-377
doi: 10.1007/s00220-015-2300-5
|
| [12] |
Hassainia Z, Masmoudi W N, Miles H. Global bifurcation of rotating vortex patches. Commun Pure Appl Math, 2020, 73(9): 1933-1980
doi: 10.1002/cpa.v73.9
|
| [13] |
Buckmaster T, Shkoller S, Vicol V. Nonuniqueness of weak solutions to the SQG equation. Commun Pure Appl Math, 2019, 72(9): 1809-1874
doi: 10.1002/cpa.v72.9
|
| [14] |
Marchand F. Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces $L^p$ or $H^{-\frac{1}{2}}$. Commun Math Phys, 2008, 277(1): 45-67
doi: 10.1007/s00220-007-0356-6
|
| [15] |
Resnick S. Dynamical Problems in Non-linear Advective Partial Differential Equations. Chicago: University of Chicago, 1995
|
| [16] |
Cao D, Qin G, Zhan W, Zou C. Existence of traveling asymmetric vortex pairs in an ideal fluid. J Differ Equations, 2023, 351(5): 131-155
doi: 10.1016/j.jde.2022.12.024
|
| [17] |
Cao D, Qin G, Zhan W, Zou C. On the global classical solutions for the generalized SQG equation. J Funct Anal, 2022, 283(2): 109503
doi: 10.1016/j.jfa.2022.109503
|
| [18] |
Arnol'd V I. Conditions for Nonlinear Stability of Stationary Plane Curvilinear Flows of an Ideal Fluid// Givental A, Khesin B, Varchenko A, et al. Vladimir I. Arnold - Collected Works. Hedelberg: Springer, 1965: 19-23
|
| [19] |
Cao D, Lai S, Zhan W. Traveling vortex pairs for 2D incompressible Euler equations. Calc Var Partial Differential Equations, 2021, 60(5): 16
doi: 10.1007/s00526-020-01890-7
|
| [20] |
Rockafellar T. Convex Analysis. Princeton, NJ: Princeton Univ Princeton Press, 1970
|
| [21] |
Lions P L. The concentration-compactness principle in the calculus of variations. The locally compact case I. Ann Inst He Poincaré, 1984, 1(2): 109-145
|
| [22] |
Lieb E H, Loss M. Analysis. Providence, RI: American Mathematical Society, 2001
|
| [23] |
Burchard A, Guo Y. Compactness via symmetrization. J Funct Anal, 2004, 214: 40-73
doi: 10.1016/j.jfa.2004.04.005
|
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