4 papers
Phase transitions for nonlinear nonlocal aggregation-diffusion equations
José A. Carrillo, Rishabh S. Gvalani
We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty…
Barriers of the McKean--Vlasov energy via a mountain pass theorem in the space of probability measures
Rishabh S. Gvalani, André Schlichting
We show that the empirical process associated with a system of weakly interacting diffusion processes exhibits a form of noise-induced metastability. The result is based on an anal…
Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis +1
We study the McKean-Vlasov equation \[ \partial_t \varrho= β^{-1} Δ\varrho + κ\nabla \cdot (\varrho \nabla (W \star \varrho)) \, , \] with periodic boundary conditions on the torus…
Emergence of stochastic dynamics in plane Couette flow
Rishabh Gvalani, Cédric Beaume
Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact…