5 citations · 5 across the 4 of their papers we have counts for
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Norm inflation and loss of regularity in negative Sobolev spaces for KdV and KP
Rémi Carles
We prove norm inflation phenomena for KdV and KP equations in negative order Sobolev spaces, in the periodic case, as well as on the whole space, on an arbitrarily large scale of n…
Propagation of coherent states in the logarithmic Schrodinger equation
Rémi Carles, Fangyuan Dong
We consider the logarithmic Schr{ö}dinger equation in a semiclassical scaling, in the presence of a smooth, at most quadratic, external potential. For initial data under the form o…
Time splitting and error estimates for nonlinear Schrodinger equations with a potential
Rémi Carles
We consider the nonlinear Schr{ö}dinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity…
On the Cauchy problem for logarithmic fractional Schr{ö}dinger equation
Rémi Carles, Fangyuan Dong
We consider the fractional Schrodinger equation with a logarithmic nonlinearity, when the power of the Laplacian is between zero and one. We prove global existence results in three…
Low regularity solutions to the logarithmic Schrodinger equation
Rémi Carles, Masayuki Hayashi, Tohru Ozawa
We consider the logarithmic Schr{ö}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is L…