American Institute of Mathematical Sciences

December  2004, 3(4): 663-674. doi: 10.3934/cpaa.2004.3.663

Steiner symmetric vortices attached to seamounts

 1 Institute for Studies in Theoretical Physics and Mathematics, Niavaran square, Tehran, Iran 2 Department of Mathematics, Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran 3 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Received  November 2003 Revised  June 2004 Published  September 2004

We prove existence of Steiner symmetric maximizers for a constrained variational problem in $\mathbb R^2$. Solutions represent steady geophysical flows over a surface of variable height. The kinetic energy is maximized with respect to the set formed by intersecting a set of rearrangements of a given function with an affine subspace of codimension one.
Citation: B. Emamizadeh, F. Bahrami, M. H. Mehrabi. Steiner symmetric vortices attached to seamounts. Communications on Pure and Applied Analysis, 2004, 3 (4) : 663-674. doi: 10.3934/cpaa.2004.3.663
 [1] J.I. Díaz, D. Gómez-Castro. Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem. Conference Publications, 2015, 2015 (special) : 379-386. doi: 10.3934/proc.2015.0379 [2] Chjan C. Lim, Junping Shi. The role of higher vorticity moments in a variational formulation of Barotropic flows on a rotating sphere. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 717-740. doi: 10.3934/dcdsb.2009.11.717 [3] Tai-Chia Lin. Vortices for the nonlinear wave equation. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 391-398. doi: 10.3934/dcds.1999.5.391 [4] Joachim Escher, Boris Kolev, Marcus Wunsch. The geometry of a vorticity model equation. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1407-1419. doi: 10.3934/cpaa.2012.11.1407 [5] Delia Ionescu-Kruse. Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 531-543. doi: 10.3934/dcds.2007.19.531 [6] Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083 [7] Andrzej Nowakowski. Variational analysis of semilinear plate equation with free boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3133-3154. doi: 10.3934/dcds.2015.35.3133 [8] Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603 [9] Filomena Feo, Pablo Raúl Stinga, Bruno Volzone. The fractional nonlocal Ornstein-Uhlenbeck equation, Gaussian symmetrization and regularity. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3269-3298. doi: 10.3934/dcds.2018142 [10] Vincenzo Ferone, Bruno Volzone. Symmetrization for fractional nonlinear elliptic problems. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022076 [11] Joseph A. Iaia. Localized radial solutions to a semilinear elliptic equation in $\mathbb{R}^n$. Conference Publications, 1998, 1998 (Special) : 314-326. doi: 10.3934/proc.1998.1998.314 [12] Ruofei Yao, Yi Li, Hongbin Chen. Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1585-1594. doi: 10.3934/dcds.2018122 [13] Yinbin Deng, Shuangjie Peng, Li Wang. Existence of multiple solutions for a nonhomogeneous semilinear elliptic equation involving critical exponent. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 795-826. doi: 10.3934/dcds.2012.32.795 [14] Constantin Christof, Christian Meyer, Stephan Walther, Christian Clason. Optimal control of a non-smooth semilinear elliptic equation. Mathematical Control and Related Fields, 2018, 8 (1) : 247-276. doi: 10.3934/mcrf.2018011 [15] Zongming Guo, Yunting Yu. Boundary value problems for a semilinear elliptic equation with singular nonlinearity. Communications on Pure and Applied Analysis, 2016, 15 (2) : 399-412. doi: 10.3934/cpaa.2016.15.399 [16] Christos Sourdis. A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart. Electronic Research Archive, 2021, 29 (5) : 2829-2839. doi: 10.3934/era.2021016 [17] Vikas S. Krishnamurthy. The vorticity equation on a rotating sphere and the shallow fluid approximation. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6261-6276. doi: 10.3934/dcds.2019273 [18] Marco Degiovanni, Michele Scaglia. A variational approach to semilinear elliptic equations with measure data. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1233-1248. doi: 10.3934/dcds.2011.31.1233 [19] Rong Xiao, Yuying Zhou. Multiple solutions for a class of semilinear elliptic variational inclusion problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 991-1002. doi: 10.3934/jimo.2011.7.991 [20] Paul H. Rabinowitz. A new variational characterization of spatially heteroclinic solutions of a semilinear elliptic PDE. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 507-515. doi: 10.3934/dcds.2004.10.507

2021 Impact Factor: 1.273