Page 568 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 568
STOCHASTIC EVOLUTION EQUATIONS (MS-68)
Nonlinear parabolic stochastic evolution equations in critical spaces
Antonio Agresti, antonio.agresti92@gmail.com
TU Kaiserslautern, Germany
Critical spaces for non-linear equations are important due to scaling invariance, and in particular
this plays a central role in fluid dynamics. In this talk we introduce and discuss local/global
well-posedness, and blow-up criteria for stochastic parabolic evolution equations in critical
spaces. Our results extend the celebrated theory of Prüss, Wilke and Simonett for deterministic
PDEs. Due to the presence of noise it is unclear that a stochastic version of the theory is
possible, but we will show that a suitable variation of the theory remains valid. We will also
explain some features which are new in both the deterministic and stochastic framework. Our
theory is applicable to a large class of semilinear and quasilinear parabolic problems which in-
cludes many of the classical SPDE. Applications to stochastic Navier-Stokes equations with
gradient noise will be also discussed.
This is a joint work with Mark Veraar (TU Delft).
Ito formulae for singular SPDEs
Carlo Bellingeri, bellinge@math.tu-berlin.de
Technische Universität Berlin, Germany
During the last years, the theory of regularity structure has become a complete theory to prove
the existence and uniqueness of a wide family of stochastic partial differential equations. In
this talk, we will discuss how to combine this theory with other probabilistic constructions to
derive some explicit Ito formula on a particular class of equations. We will focus on the additive
stochastic heat equation with additive noise and the well-known KPZ equation.
Random multiple-fragmentation and flow of particles on a surface
Lucian Beznea, lucian.beznea@imar.ro
Simion Stoilow Institute of Mathematics of the Romanian Academy and
University of Bucharest, Romania
We investigate a stochastic fragmentation processes for particles with spatial position. The
mathematical problem models the time evolution of a system of particles which move on an
Euclidean surface driven by a given force and split in fragments with smaller masses and veloc-
ities. We establish a multiple-fragmentation process and we solve the corresponding stochastic
integro-differential equation. Finally, we present several numerical simulations of such pro-
cesses. The talk is based on a joint work with Ioan R. Ionescu (Paris) and Oana Lupas¸cu-
Stamate (Bucharest).
566
Nonlinear parabolic stochastic evolution equations in critical spaces
Antonio Agresti, antonio.agresti92@gmail.com
TU Kaiserslautern, Germany
Critical spaces for non-linear equations are important due to scaling invariance, and in particular
this plays a central role in fluid dynamics. In this talk we introduce and discuss local/global
well-posedness, and blow-up criteria for stochastic parabolic evolution equations in critical
spaces. Our results extend the celebrated theory of Prüss, Wilke and Simonett for deterministic
PDEs. Due to the presence of noise it is unclear that a stochastic version of the theory is
possible, but we will show that a suitable variation of the theory remains valid. We will also
explain some features which are new in both the deterministic and stochastic framework. Our
theory is applicable to a large class of semilinear and quasilinear parabolic problems which in-
cludes many of the classical SPDE. Applications to stochastic Navier-Stokes equations with
gradient noise will be also discussed.
This is a joint work with Mark Veraar (TU Delft).
Ito formulae for singular SPDEs
Carlo Bellingeri, bellinge@math.tu-berlin.de
Technische Universität Berlin, Germany
During the last years, the theory of regularity structure has become a complete theory to prove
the existence and uniqueness of a wide family of stochastic partial differential equations. In
this talk, we will discuss how to combine this theory with other probabilistic constructions to
derive some explicit Ito formula on a particular class of equations. We will focus on the additive
stochastic heat equation with additive noise and the well-known KPZ equation.
Random multiple-fragmentation and flow of particles on a surface
Lucian Beznea, lucian.beznea@imar.ro
Simion Stoilow Institute of Mathematics of the Romanian Academy and
University of Bucharest, Romania
We investigate a stochastic fragmentation processes for particles with spatial position. The
mathematical problem models the time evolution of a system of particles which move on an
Euclidean surface driven by a given force and split in fragments with smaller masses and veloc-
ities. We establish a multiple-fragmentation process and we solve the corresponding stochastic
integro-differential equation. Finally, we present several numerical simulations of such pro-
cesses. The talk is based on a joint work with Ioan R. Ionescu (Paris) and Oana Lupas¸cu-
Stamate (Bucharest).
566
