Global existence and non-uniqueness for 3D Navier–Stokes equations with space-time white noise
We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …
McKean–Vlasov SDE and SPDE with locally monotone coefficients
W Hong, S Hu, W Liu - The Annals of Applied Probability, 2024 - projecteuclid.org
In this paper we mainly investigate the strong and weak well-posedness of a class of
McKean–Vlasov stochastic (partial) differential equations. The main existence and …
McKean–Vlasov stochastic (partial) differential equations. The main existence and …
[HTML][HTML] A stochastic PDE approach to large N problems in quantum field theory: A survey
H Shen - Journal of Mathematical Physics, 2022 - pubs.aip.org
In this Review, we review some recent rigorous results on large N problems in quantum field
theory, stochastic quantization, and singular stochastic partial differential equations (SPDEs) …
theory, stochastic quantization, and singular stochastic partial differential equations (SPDEs) …
Solving McKean-Vlasov SDES via relative entropy
Y Han - arXiv preprint arXiv:2204.05709, 2022 - arxiv.org
In this paper we explore the merit of relative entropy in proving weak well-posedness of
McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker arxiv …
McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker arxiv …
Large N Limit of the O(N) Linear Sigma Model in 3D
In this paper we study the large N limit of the O (N)-invariant linear sigma model, which is a
vector-valued generalization of the Φ 4 quantum field theory, on the three dimensional torus …
vector-valued generalization of the Φ 4 quantum field theory, on the three dimensional torus …
McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos
W Hong, S Li, W Liu - arXiv preprint arXiv:2306.15508, 2023 - arxiv.org
In this paper, we provide a general framework for investigating McKean-Vlasov stochastic
partial differential equations. We first show the existence of weak solutions by combining the …
partial differential equations. We first show the existence of weak solutions by combining the …
Lyapunov exponents and synchronisation by noise for systems of SPDEs
B Gess, P Tsatsoulis - The Annals of Probability, 2024 - projecteuclid.org
Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-
diffusion equations are proven. The treatment includes reaction potentials with degenerate …
diffusion equations are proven. The treatment includes reaction potentials with degenerate …
The Allen–Cahn equation with weakly critical random initial datum
This work considers the two-dimensional Allen–Cahn equation∂ tu= 1 2 Δ u+ mu-u 3, u (0,
x)= η (x),∀(t, x)∈[0,∞)× R 2, where the initial condition η is a two-dimensional white noise …
x)= η (x),∀(t, x)∈[0,∞)× R 2, where the initial condition η is a two-dimensional white noise …
Low temperature expansion for the Euclidean -measure
We study asymptotic expansions of the Euclidean $\Phi^ 4_2 $-measure in the low-
temperature regime. In particular, this extends the asymptotic expansions of Gaussian …
temperature regime. In particular, this extends the asymptotic expansions of Gaussian …
An SPDE approach to perturbation theory of : asymptoticity and short distance behavior
In this paper we study the perturbation theory of $\Phi^ 4_2 $ model on the whole plane via
stochastic quantization. We use integration by parts formula (ie Dyson-Schwinger equations) …
stochastic quantization. We use integration by parts formula (ie Dyson-Schwinger equations) …