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Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D
We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law,...
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Normal Crossings Singularities for Symplectic Topology: Structures
Our previous papers introduce topological notions of normal crossings symplectic divisor and variety, show that they are equivalent, in a suitable...
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On Classical Solutions of the Compressible Euler Equations for Generalized Chaplygin Gas with Qualitative Analysis
In this paper, exact classical solutions of the original three-dimensional compressible Euler equations for generalized Chaplygin gas are constructed...
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Blowup of regular solutions and \({\mathbf {C}}^{1}\) solutions for free boundary problem of Euler–Poisson equations with repulsive force in \({\mathbb {R}}^{n}\)
The compressible Euler–Poisson equations are the fundamental models in semiconductor physics and astrophysics. In this paper, by controlling the...
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On Twisted Elliptic Genera
We study the twisted elliptic genera associated to the BPS strings in the twisted circle compactification of 6d (1,0) SCFTs. Such objects can arise...
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Asymptotics of Harmonic Functions in the Absence of Monotonicity Formulas
In this article, we study the asymptotics of harmonic functions. In literature, one typical method is by proving the monotonicity of a version of...
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Boundary behavior of blowup solutions for a heat equation with a nonlinear boundary condition
This paper is concerned with positive blowup solutions for the heat equation with a nonlinear boundary condition. The result in this paper provides a...
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Hodge cohomology with a ramification filtration, I
We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors “at infinity”. We show that the...
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Cohomology of Moduli Space of Cubic Fourfolds I
In this paper we compute the cohomology of moduli space of cubic fourfolds with ADE type singularities relying on Kirwan’s blowup and Laza’s GIT...
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Existence of a ground state and blowup problem for a class of nonlinear Schrödinger equations involving mass and energy critical exponents
In this paper, we study the existence of the ground state and blowup problem for a class of nonlinear Schrödinger equations involving the mass and...
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A Blowup Criterion of the Nonhomogeneous Incompressible Asymmetric Fluids in Weak \(L^{p}\)-Spaces
This paper is concerned with Cauchy problem for the three-dimensional nonhomogeneous incompressible asymmetric fluids. A weak Serrin’s type blow-up...
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On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics
We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the...
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Further Results on Nevanlinna Hyperbolicity
Let X be a projective variety and D be an effective Cartier divisor on X . In Int J Math 32(12), Paper No. 2140015, 2021, He and Ru author introduced...
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Algebraic hyperbolicity of very general surfaces
Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification...
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How and why non smooth solutions of the 3D Navier–Stokes equations could possibly develop
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings...
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On Type I Blowups of Suitable Weak Solutions to the Navier–Stokes Equations Near Boundary
In this note, boundary Type I blowups of suitable weak solutions to the Navier–Stokes equations are discussed. In particular, it has been shown that,...