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Mild Solution for the Time-Fractional Navier–Stokes Equation Incorporating MHD Effects
Fractal and Fractional, 2022 The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence and uniqueness of the mild solution to the NS equations for the time fractional ...
Ramsha Shafqat +4 more
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Fractional evolution equation nonlocal problems with noncompact semigroups [PDF]
Opuscula Mathematica, 2016 This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations.
Xuping Zhang, Pengyu Chen
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Mild Solutions of Quantum Stochastic Differential Equations [PDF]
Electronic Communications in Probability, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
FAGNOLA, FRANCO, WILLS S. J.
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Global mild solutions of Navier‐Stokes equations [PDF]
Communications on Pure and Applied Mathematics, 2011 AbstractWe establish a global well‐posedness of mild solutions to the three‐dimensional, incompressible Navier‐Stokes equations if the initial data are in the space ${\cal{X}}^{-1}$ defined by \input amssym ${\cal{X}}^{‐1} = \{f \in {\cal{D}}^\prime(R^3): \int_{{\Bbb{R}}^3}|\xi|^{‐1}|\widehat{f}|d\xi < \infty\}$ and if the norms of the initial data ...
Lei, Zhen, Lin, Fang-Hua
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Известия Иркутского государственного университета: Серия "Математика", 2022 In this work, we will introduce a fractional Duhamel principle and use it to establish the well-boundedness and stability of a mild solution to an original fractional stochastic equation with initial data.
N. Bouteraa
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Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients [PDF]
, 2013 In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle solution of ...
Bessaih, Hakima +2 more
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A Semi-Linear Backward Parabolic cauchy Problem with Unbounded Coefficients of Hamilton-Jacobi-Bellman Type and Applications to optimal control [PDF]
, 2014 We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear ...
Addona, Davide
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Mild to Classical Solutions for XVA Equations Under Stochastic Volatility [PDF]
SSRN Electronic Journal, 2021 We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers.
Damiano Brigo +2 more
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The Burgers equation driven by a stochastic measure
Modern Stochastics: Theory and Applications, 2023 The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation.
Vadym Radchenko
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On a class of stochastic partial differential equations [PDF]
, 2015 In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a Gaussian noise ...
Song, Jian
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