Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit [PDF]
Mathematical Models and Methods in Applied Sciences, 2020 We introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto–Vicsek system and belongs to the class of Consensus-Based Optimization methods.
M. Fornasier +3 more
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Local well-posedness for the inhomogeneous nonlinear Schrödinger equation
Discrete and Continuous Dynamical Systems. Series A, 2021 We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation \begin{document}$ i\partial_t u +\Delta u = \mu |x|^{-b}|u|^\alpha u,\; u(0)\in H^s({\mathbb R}^N),\; N\geq 1,\; \mu\in {\mathbb C},\; \; b>0 $\end{document} and \begin ...
L. Aloui, S. Tayachi
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On the well-posedness problem for the derivative nonlinear Schrödinger equation [PDF]
Analysis & PDE, 2021 We consider the derivative nonlinear Schr\"odinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and $L^2$-critical with respect to scaling.
R. Killip, Maria Ntekoume, M. Vişan
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Well Posedness of New Optimization Problems with Variational Inequality Constraints
Fractal and Fractional, 2021 In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives.
Savin Treanţă
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Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption [PDF]
Communications on Pure and Applied Mathematics, 2020 We establish the well‐posedness in Gevrey function space with optimal class of regularity 2 for the three‐dimensional Prandtl system without any structural assumption.
Wei-Xi Li, N. Masmoudi, Tong Yang
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Well posedness of second-order impulsive fractional neutral stochastic differential equations
AIMS Mathematics, 2021 In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space.
Ramkumar Kasinathan +3 more
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On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations [PDF]
Communications on Pure and Applied Mathematics, 2020 We are concerned with the question of well‐posedness of stochastic, three‐dimensional, incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak–strong uniqueness; (iii ...
Martina Hofmanov'a +2 more
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Well posedness for one class of elliptic equations with drift
Boundary Value Problems, 2023 We studied one class of second-order elliptic equations with intermediate coefficient and proved that the semi-periodic problem on a strip is unique solvable in Hilbert space.
Kordan N. Ospanov
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Well posedness of magnetohydrodynamic equations in 3D mixed-norm Lebesgue space
Open Mathematics, 2022 In this paper, we introduce a new metric space called the mixed-norm Lebesgue space, which allows its norm decay to zero with different rates as ∣x∣→∞| x| \to \infty in different spatial directions.
Liu Yongfang, Zhu Chaosheng
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Local well-posedness for quasi-linear problems: A primer [PDF]
Bulletin of the American Mathematical Society, 2020 Proving local well-posedness for quasi-linear problems in partial differential equations presents a number of difficulties, some of which are universal and others of which are more problem specific.
M. Ifrim, D. Tataru
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