8,323 research outputs found
Lack of regularity of the transport density in the monge problem
In this paper, we provide a family of counterexamples to the regularity of
the transport density in the classical Monge-Kantorovich problem. We prove that
the W^{1,p} regularity of the source and target measures f ^\pm does not imply
that the transport density is W^{1,p} , that the BV regularity of f
^\pm does not imply that is BV and that f^\pm C^\infty does not
imply that is W^{1,p} , for large p
Derivation and analysis of a new 2D Green-Naghdi system
We derive here a variant of the 2D Green-Naghdi equations that model the
propagation of two-directional, nonlinear dispersive waves in shallow water.
This new model has the same accuracy as the standard Green-Naghdi
equations. Its mathematical interest is that it allows a control of the
rotational part of the (vertically averaged) horizontal velocity, which is not
the case for the usual Green-Naghdi equations. Using this property, we show
that the solution of these new equations can be constructed by a standard
Picard iterative scheme so that there is no loss of regularity of the solution
with respect to the initial condition. Finally, we prove that the new
Green-Naghdi equations conserve the almost irrotationality of the vertically
averaged horizontal component of the velocity
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