Global well-posedness for fractional Sobolev-Galpern type equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2021 This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to
Huy Tuan Nguyen, N. Tuan, Chaoxia Yang
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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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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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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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Global well‐posedness for the one‐phase Muskat problem [PDF]
Communications on Pure and Applied Mathematics, 2021 The free boundary problem for a two‐dimensional fluid permeating a porous medium is studied. This is known as the one‐phase Muskat problem and is mathematically equivalent to the vertical Hele‐Shaw problem driven by gravity force.
Hongjie Dong, F. Gancedo, Huy Q. Nguyen
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Well-posedness and tamed schemes for McKean-Vlasov Equations with Common Noise [PDF]
The Annals of Applied Probability, 2020 In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients having super-linear growth in the state variable.
C. Kumar +3 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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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 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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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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