Results 21 to 30 of about 15,258,586 (276)
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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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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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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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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Global Well Posedness for the Thermally Radiative Magnetohydrodynamic Equations in 3D
Journal of Function Spaces, 2020 In this paper, we study the thermally radiative magnetohydrodynamic equations in 3D, which describe the dynamical behaviors of magnetized fluids that have nonignorable energy and momentum exchange with radiation under the nonlocal thermal equilibrium ...
Peng Jiang, Fei Yu
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Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher [PDF]
Annales de l'Institut Fourier, 2020 The Zakharov-Kuznetsov equation in space dimension $d\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint.
S. Herr, S. Kinoshita
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On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces
Journal of Mathematics, 2021 We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space. The relations between the Levitin–Polyak well-posedness and Hadamard well-posedness for a generalized mixed variational inequality are ...
Lu-Chuan Ceng +5 more
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Well-Posedness of Triequilibrium-Like Problems
International Journal of Analysis and Applications, 2022 This work emphasizes in presenting new class of equilibrium-like problems, termed as equilibrium-like problems with trifunction. We establish some metric characterizations for the well-posed triequilibrium-like problems.
Misbah Iram Bloach +2 more
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SIAM Review, 2020 This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feed...
B. Brogliato, A. Tanwani
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Well-posedness of distribution dependent SDEs with singular drifts [PDF]
Bernoulli, 2018 In this paper we consider the following distribution dependent SDE: $$ {\mathrm d} X_t=\sigma_t(X_t,\mu_{X_t}){\mathrm d} W_t+b_t(X_t,\mu_{X_t}){\mathrm d} t, $$ where $\mu_{X_t}$ stands for the distribution of $X_t$. We show the strong well-posedness of
M. Rockner, Xicheng Zhang
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