Research
Research
Research
Research
176+ open-access research outputs.
We investigate novel scenarios of self-similar finite-time blowups of the generalized Constantin-Lax-Majda model with a parameter $a$, which are induced by a new setting where the smooth initial data …
In polar variables $(x,\theta)$ on a planar sector, we study a $(1+2)$D system (E1) derived from the two-dimensional inviscid Boussinesq equations. Under a parity/symmetry ansatz on the whole plane (o…
We establish the inviscid limit of the Yudovich solution to the heat conductive Boussinesq equation with initial velocity and temperature/buoyancy in $L^2$ and initial vorticity in $L^\infty$ on the t…
This paper presents a mathematical analysis of a one-dimensional model of turbulence based on a stochastic generalized Constantin-Lax-Majda-DeGregorio (gCLMG) equation. We focus on the specific case w…
In this paper, we study a combinatorial Ricci flow on closed pseudo $3$-manifolds $(M,\mathcal{T})$. We prove that if every edge in the triangulation $\mathcal{T}$ has valence at least $9$, then the c…
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- energy solutions below the Miura-Ju class. In particular, this shows that the s…
Vincenzo Galilei and Constantijn Huygens were both humanists and eminent musicians, the former from the late Renaissance and the latter from the early Modern era. Their respective sons, Galileo and Ch…
We investigate the Cauchy problem for a two-component generalization of the Novikov equation with cubic nonlinearity -- an integrable system whose solutions may develop strong nonlinear phenomena such…
In this manuscript, we extend Constantin-Iyer's Lagrangian formulation of Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is natural…
We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Molinet, Global Existenc…
In a widely circulated manuscript from the 1980s, now available on the arXiv, I.~G.~Macdonald introduced certain multivariable hypergeometric series ${}_pF_q(x)= {}_pF_q(x;\alpha)$ and ${}_pF_q(x,y)= …
In this paper, by means of divergence-free condition, we establish an anisotropic energy conservation class enabling one component of velocity in the largest space $L^{3} (0,T; B^{1/3}_{3,\infty})$ fo…
We characterize boundedness, compactness and Schatten class properties of generalized Volterra-type integral operators acting between large Bergman spaces $A_\omega^p$ and $A_\omega^q$ for $0 <p, q\le…
In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we fo…
The Constantin-Lax-Majda (CLM) model and the De Gregorio model which is a modification of the CLM model are well-known for their ability to emulate the behavior of the 3D Euler equations, particularly…
In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We pr…
We explore two approaches to proving existence and analyticity of solutions to nonlinear parabolic differential equations. One of these methods works well for more general nonlinearities, while the se…
Absolute continuity of polynomially bounded $n$-tuples of commuting contractions is studied. A necessary and sufficient condition is found in Constantin Apostol's "weakened $C_{0,\cdot}$ assumption", …
In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whose radial stability, …
We present exact pole dynamics solutions to the generalized Constantin-Lax-Majda (gCLM) equation in a periodic geometry with dissipation $-\Lambda^\sigma$, where its spatial Fourier transform is $\wid…
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