广义地表准地转方程的非对称行波涡对解

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Wu Wenju,Fan Boquan. Traveling Asymmetric Vortex Pairs of the Generalized Surface Quasi-Geostrophic Equation[J].Acta mathematica scientia,Series A, 2023, 43(4): 1037-1061.

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[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

Traveling Asymmetric Vortex Pairs of the Generalized Surface Quasi-Geostrophic Equation

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