17 citations · 39 across the 18 of their papers we have counts for
21 papers
A logarithmic regularity criterion for the axisymmetric Navier-Stokes equations
Stan Palasek
For axisymmetric solutions of the Navier-Stokes equations in , the circulation obeys a maximum principle, and the resulting a priori bound on is scale-inv…
Finite-time blow-up for the real-valued defocusing energy-supercritical NLW
Matthieu Cadiot, Alexandru D. Ionescu, Stan Palasek
We consider the defocusing nonlinear wave equations , with odd, for real-valued functions on , in the energy-supercritical case. For $(…
Cascade mechanisms for Navier-Stokes blow-up
Alexey Cheskidov, Mimi Dai, Stan Palasek
In a recent preprint (arXiv:2511.09556), we exhibited an inverse energy cascade for the 3D Navier-Stokes equations which results in "instantaneous" Type I blow-up and failure of un…
On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I
Alexandru D. Ionescu, Hao Jia, Stan Palasek
In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in . Our solutions are axially sym…
Finite-time blow-up in an elementary model of the 3D Navier-Stokes equations
Stan Palasek
We demonstrate finite-time blow-up in a simple, realistic shell model of the 3D Navier-Stokes equations, equipped with "smooth" (i.e., rapidly decaying in frequency) initial data a…
Instantaneous Type I blow-up and non-uniqueness of smooth solutions of the Navier-Stokes equations
Alexey Cheskidov, Mimi Dai, Stan Palasek
For any smooth, divergence-free initial data, we construct a solution of the Navier--Stokes equations that exhibits Type~I blow-up of the norm at time , while rem…
Arbitrary norm growth in the 3D Navier-Stokes equations
Stan Palasek
We construct a family of smooth initial data for the Navier-Stokes equations, bounded in , that gives rise to arbitrarily large global solutions. As a conseq…
Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data
Matei P. Coiculescu, Stan Palasek
We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space from which there exist…
Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model
Stan Palasek
The uniqueness of Leray-Hopf solutions to the incompressible Navier-Stokes equations remains a significant open question in fluid mechanics. This paper proposes a potential mechani…
Non-uniqueness up to the Onsager threshold for the forced SQG equation
Aynur Bulut, Manh Khang Huynh, Stan Palasek
We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imp…
Convex integration above the Onsager exponent for the forced Euler equations
Aynur Bulut, Manh Khang Huynh, Stan Palasek
We establish new non-uniqueness results for the Euler equations with external force on . By introducing a novel alternating convex integration scheme, we…
Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak norm
W. S. Ożański, S. Palasek
We are concerned with strong axisymmetric solutions to the D incompressible Navier-Stokes equations. We show that if the weak norm of a strong solution on the time int…
Epochs of regularity for wild Hölder-continuous solutions of the Hypodissipative Navier-Stokes System
Aynur Bulut, Manh Khang Huynh, Stan Palasek
We consider the hypodissipative Navier-Stokes equations on and seek to construct non-unique, Hölder-continuous solutions with epochs of regularity (smoo…
A minimum critical blowup rate for the high-dimensional Navier-Stokes equations
Stan Palasek
We prove quantitative regularity and blowup theorems for the incompressible Navier-Stokes equations in , when the solution lies in the critical space $L_t^\in…
Improved quantitative regularity for the Navier-Stokes equations in a scale of critical spaces
Stan Palasek
We prove a quantitative regularity theorem and blowup criterion for classical solutions of the three-dimensional Navier-Stokes equations satisfying certain critical conditions. The…
A Reputation-Based Model for Decision-Making in Online Social Networks
Stan Palasek
The online exchange of social recognition including, for instance, the Facebook "like" appears to produce a scarce allocation without a clear utility function defined for anyone in…
Measuring Prestige in Online Social Networks
Stan Palasek
We study the locally-defined social capital metric of Palasek (2013) for determining individuals' prestige within an online social network. From it we derive an equivalent global m…
Non-Cooperativity in Bayesian Social Learning
Stan Palasek
We describe a Bayesian model for social learning of a random variable in which agents might observe each other over a directed network. The outcomes produced are compared to those…
Arbitrage-free exchange rate ensembles over a general trade network
Stan Palasek
It is assumed that under suitable economic and information-theoretic conditions, market exchange rates are free from arbitrage. Commodity markets in which trades occur over a compl…
On the Strategic Allocation of Social Gratification
Stan Palasek
Members of social networks are given opportunities to bestow positive recognition upon one another by means of constructs such as "likes" and "retweets." Although recipients no dou…
Primordial RNA Replication and Applications in PCR Technology
Stan Palasek
The emergence of self-replication and information transmission in life's origin remains unexplained despite extensive research on the topic. A hypothesis explaining the transition…