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Behavior of solutions of 2D quasi-geostrophic equations
We study solutions to the 2D quasi-geostrophic (QGS) equation $$ \frac{\partial \theta}{\partial t}+u\cdot\nabla\theta + \kappa (-\Delta)^{\alpha}\theta=f $$ and prove global existence and uniquenessExpand
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AI Challenger : A Large-scale Dataset for Going Deeper in Image Understanding
TLDR
This paper proposed a large-scale dataset named AIC (AI Challenger) with three sub-datasets, human keypoint detection (HKD), large- scale attribute dataset (LAD) and image Chinese captioning (ICC). Expand
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Generalized MHD equations
  • J. Wu
  • Mathematics
  • 10 December 2003
Abstract Solutions of the d-dimensional generalized MHD (GMHD) equations ∂ t u+u· ∇ u=− ∇ P+b· ∇ b−ν(− Δ ) α u, ∂ t b+u· ∇ b=b· ∇ u−η(− Δ ) β b are studied in this paper. We pay special attention toExpand
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Identification of Anthropogenic and Natural Inputs of Sulfate and Chloride into the Karstic Ground Water of Guiyang, SW China: Combined δ37Cl and δ34S Approach
Because of active exchange between surface and groundwater of a karstic hydrological system, the groundwater of Guiyang, the capital city of Guizhou Province, southwest China, has been seriouslyExpand
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Global Regularity for a Class of Generalized Magnetohydrodynamic Equations
  • J. Wu
  • Mathematics
  • 1 June 2011
It remains unknown whether or not smooth solutions of the 3D incompressible MHD equations can develop finite-time singularities. One major difficulty is due to the fact that the dissipation given byExpand
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Two regularity criteria for the 3D MHD equations
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requiresExpand
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Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
Abstract We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical ( α 1 / 2 ) dissipation ( − Δ ) α : If a Leray–Hopf weak solution is HolderExpand
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Regularity Criteria for the Generalized MHD Equations
  • J. Wu
  • Mathematics
  • 31 January 2008
This paper derives regularity criteria for the generalized magnetohydrodynamics (MHD) equations, a system of equations resulting from replacing the Laplacian −Δ in the usual MHD equations by aExpand
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A Large-Scale Attribute Dataset for Zero-Shot Learning
TLDR
We propose a Large-scale Attribute Dataset (LAD) with 78,017 images of 230 classes. Expand
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Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces
  • J. Wu
  • Mathematics
  • 1 May 2006
When estimating solutions of dissipative partial differential equations in Lp-related spaces, we often need lower bounds for an integral involving the dissipative term. If the dissipative term isExpand
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