Results 31 to 40 of about 1,955 (98)
, 2014 We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to
Chae, Dongho +2 more
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Abstract and Applied AnalysisMSC2020 Classification: 35R11, 35B06 ...
Yu-Cheng An, Guai-Qi Tian
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Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
Advanced Nonlinear Studies, 2023 We investigate the rigidity of global minimizers u≥0u\ge 0 of the Alt-Phillips functional involving negative power potentials ∫Ω(∣∇u∣2+u−γχ{u>0})dx,γ∈(0,2),\mathop{\int }\limits_{\Omega }(| \nabla u{| }^{2}+{u}^{-\gamma }{\chi }_{\left\{u\gt 0\right\}}){\
De Silva Daniela, Savin Ovidiu
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A Note on Div-Curl Lemma [PDF]
, 2007 2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and $$div(u^−v^→) ∈ H^1(R^d)$$ which include
Gala, Sadek
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The regularity of weak solutions for certain n-dimensional strongly coupled parabolic systems
Advanced Nonlinear Studies, 2022 This paper is concerned with the n-dimensional strongly coupled parabolic systems with triangular form in the cylinder Ω×(0,T]\Omega \times (0,T]. We investigate L2{L}^{2} and Hölder regularity of the derivatives of weak solutions (u1,u2)\left({u}_{1},{u}
Tan Qi-Jian
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On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations [PDF]
, 2012 2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.We derive analytic estimates and holomorphic extensions for the solutions of a class of elliptic pseudodifferential equations on ...
Cappiello, Marco, Nicola, Fabio
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Transference of fractional Laplacian regularity
, 2014 In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus $\mathbb{T}^n$ from the fractional Laplacian on $\mathbb{R}^n$.
J.E. Galé +4 more
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Sobolev-Kantorovich Inequalities
Analysis and Geometry in Metric Spaces, 2015 In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich ...
Ledoux Michel
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Advances in Nonlinear Analysis, 2020 We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group.
Wang Jialin +3 more
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Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation
Advances in Nonlinear Analysis, 2023 In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: (−Δ)su=λu+α(Iμ*∣u∣q)∣u∣q−2u+(Iμ*∣u∣2μ,s*)∣u∣2μ,s*−2u,inRN,{\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u|
Lan Jiali, He Xiaoming, Meng Yuxi
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