期刊
ANNALES DE L INSTITUT FOURIER
卷 58, 期 3, 页码 945-988出版社
ANNALES INST FOURIER
DOI: 10.5802/aif.2375
关键词
Camassa-Holm equation; periodic solution
类别
We show that the periodic Camassa-Holm equation u(t) - u(xxt) + 3uu(x)-2u(x)u(xx)-uu(xxx) = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u vertical bar(t=0) in H-per(1). The result is obtained by introducing per a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure mu with mu(ac), = (u(2) + u(x)(2))dx. The total energy is preserved by the solution.
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