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math.AP2024★ 3 cited
Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data
Patrick Gérard, Enno Lenzmann
We study the energy-critical half-wave maps equation: \[ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} \] for . O…
math.AP2024★ 1 cited
The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in is obtained explicitly for generic rati…
math.AP2024★ 1 cited
The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
We show that the initial-value problem for the Benjamin-Ono equation on with rational initial data with only simple poles can be solved in closed for…