Global existence of H¹ martingale solutions to the stochastic Camassa-Holm equation is shown via viscous Galerkin approximations, tightness, and Skorokhod-Jakubowski representations.
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Proves almost sure continuous dependence of the solution map on initial data in H^s (s>3/2) and existence of non-unique invariant measures for the Camassa-Holm equation with linear multiplicative noise.
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.
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Global Existence of Weak Martingale Solutions to the Camassa-Holm Equation with Linear Multiplicative Noise
Global existence of H¹ martingale solutions to the stochastic Camassa-Holm equation is shown via viscous Galerkin approximations, tightness, and Skorokhod-Jakubowski representations.
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Invariant Measure of the Camassa-Holm Equation with Linear Multiplicative Noise
Proves almost sure continuous dependence of the solution map on initial data in H^s (s>3/2) and existence of non-unique invariant measures for the Camassa-Holm equation with linear multiplicative noise.
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Soliton-like solutions of the Camassa--Holm equation with variable coefficients and a small dispersion
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.