21 citations · 64 across the 14 of their papers we have counts for
8 papers · 1 filter
Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
Diego Alonso-Orán, Peter H. C. Pang, Hao Tang
In this paper we investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa-Holm equation i…
The viscous variational wave equation with transport noise
Peter H. C. Pang
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove p…
Second order commutator estimates in renormalisation theory for SPDEs with gradient-type noise
Peter H. C. Pang
An important step in standard renormalisation arguments involve convolution against a standard mollifier. As pointed out in (Punshon-Smith--Smith 2018), this generates second order…
Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
Luca Galimberti, Helge Holden, Kenneth H. Karlsen +1
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term.…
Global well-posedness of the viscous Camassa--Holm equation with gradient noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position…
The Hunter-Saxton equation with noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter-Saxton equatio, and prove several properties of the blow-up of its solutions. An import…
Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
Gui-Qiang G. Chen, Peter H. C. Pang
Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and…
Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing
Gui-Qiang G. Chen, Peter H. C. Pang
We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A…