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8 papers · 2 filters
Two soliton solutions to the three dimensional gravitational Hartree equation
Joachim Krieger, Yvan Martel, Pierre Raphael
We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the…
Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model
Patrick Cattiaux, Djalil Chafai, Sébastien Motsch
The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of…
Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system
Tomasz Cieślak, Philippe Laurençot
Finite time blow-up is shown to occur for solutions to a one-dimensional quasilinear parabolic-parabolic chemotaxis system as soon as the mean value of the initial condition exceed…
Finite time blow-up for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system
Tomasz Cieślak, Philippe Laurençot
Finite time blow-up is shown to occur for radially symmetric solutions to a critical quasilinear Smoluchowski-Poisson system provided that the mass of the initial condition exceeds…
Proteus mirabilis swarm-colony development with drift
Philippe Laurençot, Christoph Walker
We prove a global existence result for a model describing the swarming phenomenon of the bacterium Proteus mirabilis. The model consists of an ordinary differential equation couple…
On Stability of Pseudo-Conformal Blowup for L^2-critical Hartree NLS
Joachim Krieger, Enno Lenzmann, Pierre Raphael
We consider -critical focusing nonlinear Schroedinger equations with Hartree type nonlinearity $$i \pr_t u = -\DD u - \big (Φ\ast |u|^2 \big) u \quad {in $\RR^4$},$$ where $Φ(…