Quasilinear rough partial differential equations with transport noise

Pathwise mild solutions for quasilinear stochastic partial differential equations

(2020) Christian Kuehn et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

A Solution Theory for Quasilinear Singular SPDEs

(2019) Máté Gerencsér et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Well-Posedness of Nonlinear Diffusion Equations with Nonlinear, Conservative Noise

(2019) Benjamin Fehrman et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Paracontrolled quasilinear SPDEs

(2019) Marco Furlan et al.   ANNALS OF PROBABILITY

A priori estimates for rough PDEs with application to rough conservation laws

(2019) Aurélien Deya et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Generalized Burgers equation with rough transport noise

(2019) Antoine Hocquet et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions

(2019) Jonas M. Tölle   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Stochastic nonlinear Fokker–Planck equations

(2019) Michele Coghi et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential

(2018) Giuseppe Cannizzaro et al.   ANNALS OF PROBABILITY

An energy method for rough partial differential equations

(2018) Antoine Hocquet et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE

(2018) Benjamin Gess et al.   ANNALS OF PROBABILITY

On the Navier–Stokes equation perturbed by rough transport noise

(2018) Martina Hofmanová et al.   JOURNAL OF EVOLUTION EQUATIONS

Quasilinear SPDEs via Rough Paths

(2018) Felix Otto et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Perron’s method for pathwise viscosity solutions

(2018) Benjamin Seeger   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness

(2017) Martina Hofmanová et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Stochastic non-isotropic degenerate parabolic–hyperbolic equations

(2017) Benjamin Gess et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Degenerate parabolic stochastic partial differential equations: Quasilinear case

(2016) Arnaud Debussche et al.   ANNALS OF PROBABILITY

Long-Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws

(2016) Benjamin Gess et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise

(2016) Ioana Ciotir et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Averaging along irregular curves and regularisation of ODEs

(2016) R. Catellier et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Scalar conservation laws with multiple rough fluxes

(2015) Benjamin Gess et al.   Communications in Mathematical Sciences

Rough paths and 1d SDE with a time dependent distributional drift: application to polymers

(2015) François Delarue et al.   PROBABILITY THEORY AND RELATED FIELDS

A theory of regularity structures

(2014) M. Hairer   INVENTIONES MATHEMATICAE

Solving the KPZ equation

(2013) Martin Hairer   ANNALS OF MATHEMATICS

Rough path stability of (semi-)linear SPDEs

(2013) Peter Friz et al.   PROBABILITY THEORY AND RELATED FIELDS

Rough evolution equations

(2010) Massimiliano Gubinelli et al.   ANNALS OF PROBABILITY

Scalar conservation laws with stochastic forcing

(2010) A. Debussche et al.   JOURNAL OF FUNCTIONAL ANALYSIS