52 citations · 207 across the 36 of their papers we have counts for
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Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known whe…
Global existence of weak solutions to the Navier-Stokes-Korteweg equations
Paolo Antonelli, Stefano Spirito
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of fin…
On smooth approximations of rough vector fields and the selection of flows
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
In this work we deal with the selection problem of flows of an irregular vector field. We first summarize an example from \cite{CCS} of a vector field and a smooth approximatio…
Smooth approximation is not a selection principle for the transport equation with rough vector field
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the…