In his seminal work, Leray demonstrated the existence of global
weak solutions, with nonincreasing energy, to the Navier-Stokes
equations in three dimensions. In this talk we exhibit two distinct
Leray solutions with zero initial velocity and...
We determine the average size of the 3-torsion in class groups
of G-extensions of a number field when G is any transitive 2-group
containing a transposition, for example, D4. It follows from
the Cohen--Lenstra--Martinet heuristics that the average...
Whether the 3D incompressible Euler equations can develop a
finite-time singularity from smooth initial data is an outstanding
open problem. The presence of vortex stretching is the primary
source of a potential finite-time singularity. However, to...
The viscosity of a fluid is usually a constant, independent of
the stress. There are however in nature several examples of fluids
(ice, molten lava, blood, certain polymers, some salt
solutions) where viscosity changes under applied forces.
Such...
A key discovery from the past six decades of solar system
exploration is that liquid water oceans may be a common planetary
phenomenon. At least six ice-covered moons of the outer solar
system present compelling evidence for subsurface oceans,
and...
We discuss recent mathematical constructions of self-similar
gravitational collapse for Newtonian stars governed by the
Euler-Poisson system, known as Larson-Penston solutions for the
isothermal stars and Yahil solutions for polytropic stars,
and...
It is known since the work of Dyachenko & Zakharov
that for the weakly nonlinear 2d infinite depth water waves, there
are no 3-wave interactions and all of the 4-wave interaction
coefficients vanish on the non-trivial resonant manifold. In
this...
The lecture will discuss a joint work with Gregorio Baldi and
Bruno Klingler. Given a polarized Z-VHS over a complex,
smooth quasi-projective variety S, we describe some properties of
the Hodge locus, a countable union of algebraic subvarieties
of...
In this talk we consider the pressureless Euler system in
dimension greater than or equal to two. Several works have been
devoted to the search of solutions which satisfy the following
adhesion or sticky particle principle: if two particles of
the...
In this talk we will present a construction of global existence
of small solutions of the modified SQG equations, close to the
disk. The proof uses KAM theory and a Nash-Moser argument, and does
not involve any external parameters. We moreover prove...
