Global well‐posedness of the 3D hydrostatic magnetohydrodynamics equations
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DOI: 10.1002/mma.10109
Abstract: In this paper, the three‐dimensional hydrostatic magnetohydrodynamic (HMHD) equations are considered on a thin domain. We showed the global existence and uniqueness (regularity) of strong solutions to the three‐dimensional incompressible HMHD equations without any small… read more here.
Keywords: well posedness; magnetohydrodynamics; magnetohydrodynamics equations; posedness hydrostatic ... See more keywords
Global Well‐Posedness of Landau–Lifshitz Flow With External Electromagnetic Field for Small Data in Three Dimensions
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DOI: 10.1002/mma.10915
Abstract: The Landau–Lifshitz–Maxwell system is an important model in magnetic storage devices, where the magnetization is affected by external electromagnetic fields. In this article, we are interested in the special case of the coupled system, that… read more here.
Keywords: landau lifshitz; small data; well posedness; external electromagnetic ... See more keywords
Global well‐posedness and asymptotics of full compressible non‐resistive magnetohydrodynamics system with large external potential forces
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7774
Abstract: We consider the global well‐posedness and asymptotic behavior of compressible viscous, heat‐conductive, and non‐resistive magnetohydrodynamics (MHD) fluid in a field of external forces over three‐dimensional periodic thin domain Ω=𝕋2×(0,δ) . The unique existence of the… read more here.
Keywords: resistive magnetohydrodynamics; system; non resistive; well posedness ... See more keywords
Fostering Global Well‐Being: Insights From India on Learned Happiness for Administrators and Education Policy‐Makers
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DOI: 10.1002/pa.70059
Abstract: A nation can make great strides in progress when the happiness of all its residents is prioritized. This is because happiness is the driving force behind improved mental health, enhanced creativity, heightened awareness, and the… read more here.
Keywords: fostering global; happiness curriculum; happiness; insights india ... See more keywords
Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance
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DOI: 10.1007/s00208-025-03121-w
Abstract: In this paper, we consider the nonlinear Schrödinger equation (NLS) with a general homogeneous nonlinearity in dimensions up to three. We assume that the degree (i.e., power) of the nonlinearity is such that the equation… read more here.
Keywords: schr dinger; space; well posedness; weighted space ... See more keywords
Global well-posedness for the fifth-order mKdV equation
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-018-7241-4
Abstract: AbstractWe prove the global well-posedness for the Cauchy problem of fifth-order modified Korteweg–de Vries equation in Sobolev spaces Hs(ℝ) for s > $$ - \frac{3}{{22}}$$−322 . The main approach is the “I-method” together with the… read more here.
Keywords: order mkdv; global well; fifth order; well posedness ... See more keywords
Global Well-Posedness for a 1-D Compressible Non-isothermal Model for Nematic Liquid Crystals
Sign Up to like & getrecommendations! Published in 2019 at "Acta Applicandae Mathematicae"
DOI: 10.1007/s10440-019-00285-x
Abstract: In this paper, we prove global well-posedness of strong solutions to a 1-D compressible non-isothermal model for nematic liquid crystals, provided that the initial datum satisfies a natural compatibility condition. The initial density may vanish… read more here.
Keywords: isothermal model; global well; model nematic; compressible non ... See more keywords
Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schrödinger Equations
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DOI: 10.1007/s10884-018-9709-4
Abstract: We study the global Cauchy problem for the nonlinear Schrödinger equations in the Sobolev space of fractional order. In particular, we show the global well-posedness and the analytic smoothing effect for global solutions to a… read more here.
Keywords: nonlinear schr; dinger equations; global well; well posedness ... See more keywords
Global well-posedness of the MHD boundary layer equations in the Sobolev space
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DOI: 10.1007/s11425-025-2456-6
Abstract: We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel… read more here.
Keywords: well posedness; boundary layer; mhd boundary; layer equations ... See more keywords
Energy estimates and global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients singular in time
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Pseudo-Differential Operators and Applications"
DOI: 10.1007/s11868-021-00439-2
Abstract: The goal of this paper is to establish a global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients in $$C^2((0,T];C^\infty ({{\mathbb {R}}}^n))$$ C 2 ( ( 0 , T ] ;… read more here.
Keywords: strictly hyperbolic; posedness broad; well posedness; broad class ... See more keywords
Global well-posedness and long-time behavior of the fractional NLS
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DOI: 10.1007/s40072-021-00210-0
Abstract: In this paper, our discussion mainly focuses on equations with energy supercritical nonlinearities. We establish probabilistic global well-posedness (GWP) results for the cubic Schrödinger equation with any fractional power of the Laplacian in all dimensions.… read more here.
Keywords: behavior fractional; posedness long; global well; time behavior ... See more keywords