On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces [PDF]
Communications in Partial Differential Equations, 2019 We investigate the existence and uniqueness issues of the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial velocity u0 and magnetic field B0 in critical regularity spaces.
R. Danchin, Jin Tan
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Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds
Advances in Nonlinear Analysis, 2023 In this article, we study the long-time dynamical behavior of the solution for a class of semilinear edge-degenerate parabolic equations on manifolds with edge singularities. By introducing a family of potential well and compactness method, we reveal the
Chen Yuxuan
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On Singular Vortex Patches, I: Well-posedness Issues [PDF]
Memoirs of the American Mathematical Society, 2019 The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness.
T. Elgindi, In-Jee Jeong
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α-Well-Posedness for Mixed Quasi Variational-Like Inequality Problems
Abstract and Applied Analysis, 2011 The concepts of α-well-posedness, α-well-posedness in the generalized sense, L-α-well-posedness and L-α-well-posedness in the generalized sense for mixed quasi variational-like inequality problems are investigated.
Jian-Wen Peng, Jing Tang
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Well-posedness and numerical algorithm for the tempered fractional differential equations
Discrete & Continuous Dynamical Systems - B, 2019 Trapped dynamics widely appears in nature, e.g., the motion of particles in viscous cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting time distribution (having diverging first moment) describes this phenomenon. Because
Can Li, W. Deng, Lijing Zhao
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Well posedness and convergence analysis of the ensemble Kalman inversion [PDF]
Inverse Problems, 2018 The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various areas of ...
D. Blömker +3 more
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Generic well-posedness in minimization problems
Abstract and Applied Analysis, 2005 The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how
A. Ioffe, R. E. Lucchetti
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Singularity formation and global Well-posedness for the generalized Constantin–Lax–Majda equation with dissipation [PDF]
Nonlinearity, 2019 We study a generalization due to De Gregorio and Wunsch et al of the Constantin–Lax–Majda equation (gCLM) on the real line where H is the Hilbert transform and .
Jiajie Chen
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Well-posedness of the hydrostatic Navier–Stokes equations [PDF]
Analysis & PDE, 2018 We address the local well-posedness of the hydrostatic Navier-Stokes equations. These equations, sometimes called reduced Navier-Stokes/Prandtl, appear as a formal limit of the Navier-Stokes system in thin domains, under certain constraints on the aspect
D. Gérard-Varet, N. Masmoudi, V. Vicol
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No‐regret and low‐regret control for a weakly coupled abstract hyperbolic system
Asian Journal of Control, EarlyView.Abstract This paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave‐like phenomena and complexity, become even more challenging with weak coupling between subsystems.
Meriem Louafi +3 more
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