SDEs with critical time dependent drifts: Weak solutions

Röckner, Michael; Zhao, Guohuan

doi:10.3150/22-bej1478

Cited by 8 publications

(1 citation statement)

References 29 publications

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“…We also refer the reader to Chapters 12 and 15 of Lemarié-Rieusset [40]. Similar criteria have been established for other types of problems, spanning from the study of MHD equations Jia and Zhou [37] to stochastic differential equations Neves and Olivera [46]; Krylov and Röckner [39]; Rööckner and Zhao [51]. We notice that the proof of Theorem 1.1 is fully quantitative whereas the endpoint proof of Iskauriaza et al [35] is obtained by contradiction and thanks to a compactness argument (we refer to the recent contributions Tao [56]; Palasek [49] for a quantitative approach of the same result).…”

Section: Link Between the Landau Equation And The Navier-stokes Equationmentioning

confidence: 70%

A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

Alonso,

Bagland,

Desvillettes

et al. 2024

Arch Rational Mech Anal

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In this paper, we introduce Prodi–Serrin like criteria which enable us to provide a priori estimates for the solutions to the spatially homogeneous Landau equation for all classical soft potentials and dimensions $$d \geqq 3$$ d ≧ 3 . The physical case of Coulomb interaction in dimension $$d=3$$ d = 3 is included in our analysis; this generalizes the work of Silvestre (J Differ Equ 262:3034–3055, 2017). Our approach is quantitative and does not require a preliminary knowledge of elaborate tools for nonlinear parabolic equations.

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Section: Link Between the Landau Equation And The Navier-stokes Equationmentioning

confidence: 70%

A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

Alonso,

Bagland,

Desvillettes

et al. 2024

Arch Rational Mech Anal

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Form-Boundedness and SDEs with Singular Drift

Kinzebulatov

2024

Springer INdAM Series

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Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

Kalinin,

Meyer-Brandis,

Proske

2024

J Theor Probab

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We deduce stability and pathwise uniqueness for a McKean–Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz continuous drift and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients, we provide unique strong solutions even if the drift fails to be of affine growth. The theory that we develop rests on Itô’s formula and leads to pth moment and pathwise exponential stability for $$p\ge 2$$ p ≥ 2 with explicit Lyapunov exponents.

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SDEs with critical time dependent drifts: Weak solutions

Cited by 8 publications

References 29 publications

A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

Form-Boundedness and SDEs with Singular Drift

Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

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