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The support of the momentum density of the Camassa-Holm equation. (English) Zbl 05992325
Summary: Bounds for the size of the support of a compactly supported momentum density of the Camassa – Holm equation are derived. This is achieved by estimating the first Dirichlet eigenvalue of the support. This elaborates the result on the preservation of its compactness, and gives more information on the velocity by estimating the size of the region where it is not that well understood.
76Fluid mechanics
[1]Constantin, A.: Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Ann. inst. Fourier (Grenoble) 50, 321-362 (2000) · Zbl 0944.35062 · doi:10.5802/aif.1757 · doi:numdam:AIF_2000__50_2_321_0
[2]Constantin, A.; Escher, J.: Global existence and blow-up for a shallow water equation, Ann. sc. Norm. super. Pisa cl. Sci. 26, No. 2, 303-328 (1998) · Zbl 0918.35005 · doi:numdam:ASNSP_1998_4_26_2_303_0
[3]Constantin, A.: Finite propagation speed for the Camassa–Holm equation, J. math. Phys., 023506 (2005) · Zbl 1076.35109 · doi:10.1063/1.1845603
[4]Henry, D.: Compactly supported solutions of the Camassa–Holm equation, J. nonlinear math. Phys. 12, 342-347 (2005) · Zbl 1086.35079 · doi:10.2991/jnmp.2005.12.3.3
[5]Y. Zhou, Infinite propagation speed for a shallow water equation, Preprint, 2005. Available at http://www.fim.math.ethz.ch/preprints/2005/zhou.pdf.
[6]Himonas, A. A.; Misiolek, G.; Ponce, G.; Zhou, Y.: Persistence properties and unique continuation of solutions of the Camassa–Holm equation, Comm. math. Phys. 271, 511-522 (2007) · Zbl 1142.35078 · doi:10.1007/s00220-006-0172-4
[7]Kim, N.: Eigenvalues associated with the vortex patch in 2-D Euler equations, Math. ann. 330, 747-758 (2004) · Zbl 1058.76012 · doi:10.1007/s00208-004-0568-4
[8]Constantin, A.; Lannes, D.: The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equation, Arch. ration. Mech. anal. 192, 165-186 (2009) · Zbl 1169.76010 · doi:10.1007/s00205-008-0128-2
[9]Lai, S.; Wu, Y.: Global solutions and blow-up phenomena to a shallow water equation, J. differential equations 249, 693-706 (2010) · Zbl 1198.35041 · doi:10.1016/j.jde.2010.03.008
[10]Constantin, A.; Escher, J.: Wave breaking for nonlinear nonlocal shallow water equations, Acta math. 181, 229-243 (1998) · Zbl 0923.76025 · doi:10.1007/BF02392586
[11]Camassa, R.; Holm, D.: An integrable shallow water equation with peaked solitons, Phys. rev. Lett. 71, 1661-1664 (1993) · Zbl 0972.35521 · doi:10.1103/PhysRevLett.71.1661