×

zbMATH — the first resource for mathematics

The support of the momentum density of the Camassa-Holm equation. (English) Zbl 1408.35165
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.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
[2] Constantin, A.; Escher, J., Global existence and blow-up for a shallow water equation, Ann. sc. norm. super. Pisa cl. sci., 26, 2, 303-328, (1998) · Zbl 0918.35005
[3] Constantin, A., Finite propagation speed for the camassa – holm equation, J. math. phys., 023506, (2005) · Zbl 1076.35109
[4] Henry, D., Compactly supported solutions of the camassa – holm equation, J. nonlinear math. phys., 12, 342-347, (2005) · Zbl 1086.35079
[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
[7] Kim, N., Eigenvalues associated with the vortex patch in 2-D Euler equations, Math. ann., 330, 747-758, (2004) · Zbl 1058.76012
[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
[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
[10] Constantin, A.; Escher, J., Wave breaking for nonlinear nonlocal shallow water equations, Acta math., 181, 229-243, (1998) · Zbl 0923.76025
[11] Camassa, R.; Holm, D., An integrable shallow water equation with peaked solitons, Phys. rev. lett., 71, 1661-1664, (1993) · Zbl 0972.35521
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.