New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can get twisted, warped or direct decompositions. Some applications to Lorentzian man…
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16 results for “irrotational”
Some remarks on quasi generalized CR-null geometry in indefinite nearly cosymplectic manifoldsmath.DG
Study characterizes geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
problem Characterizing geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
method Characterization through totally umbilical and irrotational properties, and discussion of geodesity conditions.
result Characterizes geometric properties of ascreen QGCR-null submanifolds.
NOHD optimizes multi-agent systems by decomposing dynamics into irrotational and solenoidal components.
problem Non-stationarity and conflicting interests in multi-agent learning problems.
method NOHD (Newton Optimization on Helmholtz Decomposition) decomposes system dynamics into irrotational and solenoidal components.
result NOHD ensures quadratic convergence in purely irrotational and solenoidal systems and attracts to stable fixed points in general multi-agent systems.
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…
We review geometrical properties of a static spacetime , including geodesic completeness, causality, standard splittings, compact , closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients , (, being a …
We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, i…
A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl …
The paper analyzes the score field of diffusion models using Burgers dynamics.
problem Understanding the evolution of score fields in diffusion models.
method Analyzes the score field through Burgers-type evolution law for diffusion models.
result Identifies a universal \( anh\) interfacial term in the score field.
Gradient η-Ricci solitons on warped products are studied.
problem Characterizing and constructing gradient η-Ricci solitons on warped product manifolds.
method Using Bochner formula and properties of gradient vector fields, derive a Laplacian equation and construct solitons.
result Gradient η-Ricci solitons on warped products are completely determined by a potential function under certain conditions.
In this paper we study some global properties of static potentials on asymptotically flat -manifolds in the nonvacuum setting. Heuristically, a static potential represents the (signed) length along of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…
The classical theory of Riemann ellipsoids is formulated naturally as a gauge theory based on a principal G-bundle . The structure group G=SO(3) is the vorticity group, and the bundle ${\cal P}=GL_+(3, R})$ is the connected component of the general linear group. The base manifold is the space of positive-defi…
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
New estimates quantify blow-up rates of spacelike singularities in gravitational collapse.
problem Quantifying the blow-up rates of spacelike singularities in gravitational collapse.
method Deriving new quantitative estimates using spherical symmetry and double-null coordinates.
result Polynomial blow-up rates for various quantities, with improved estimates for and .
The universe's shape and size are determined in general cosmological models.
problem Determining the shape and size of the universe in general cosmological models.
method Using differential geometry and extensions of the Bonnet-Myers theorem, the researchers derived conditions for a finite universe and provided a list of possible topologies.
result The spatial sections of the universe can be either , , , , or covered by the sphere or torus .
Energy Matching unifies flow matching and energy-based models for generative modeling.
problem Inability of flow-based models to integrate partial observations and priors.
method Energy Matching framework that integrates flow matching and energy-based models.
result Substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation.
Local well-posedness proved for 3D compressible Euler equations with rough vorticity.
problem Proving local well-posedness for compressible Euler equations with rough vorticity.
method Decomposing velocity into irrotational and wave components, using cancellations, trilinear estimates, and Strichartz estimates.
result Local well-posedness achieved for compressible Euler equations in with for rough vorticity.