相关论文: Square function and heat flow estimates on domains
The paper considers the heat transfer characteristics of a thin film flow over a hot horizontal flat plate resulting from a cold vertical liquid jet falling onto a surface. A numerical solution of high accuracy is obtained for large…
The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts…
We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.
We prove square function estimates for certain conical regions. Specifically, let $\{\Delta_j\}$ be regions of the unit sphere $\mathbb{S}^{n-1}$ and let $S_j f$ be the smooth Fourier restriction of $f$ to the conical region…
The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials…
We carry out direct numerical simulation (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case of unit Prandtl number. Reynolds numbers up to $Re_\tau \approx 2000$ are considered which are much…
A generalized physics-based expression for the drag coefficient of spherical particles moving in a fluid is derived. The proposed correlation incorporates essential rarefied physics, low-speed hydrodynamics, and shock-wave physics to…
In this paper, we derive a simple sum rule satisfied by the gluon spectral function at finite temperature. This sum rule is useful in order to calculate exactly some integrals that appear frequently in the photon or dilepton production rate…
We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H\"older continuous functions. As an application we solve the Dirichlet and…
An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A…
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
We relate Gruet formula for the heat kernel on real hyperbolic spaces to the commonly used one derived from Millson induction. The bridge between both formulas is settled by Yor result on the joint distribution of a Brownian motion and of…
We prove strong-type $A_p$-$A_\infty$ estimate for square functions, improving on the $ A_p$ bound due to Lerner. Entropy bounds, in the recent innovation of Treil-Volberg, are then proved. The techniques of proof include parallel stopping…
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by F\"uhrer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present…
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between…
We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being…
We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function maps $L^{p}$ into…
The paper contains the proof of $L^p$-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit…
The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the…