陶哲轩教你学物理Lec 3.1 Weak Solution 潘润琦 一只菜鸡 木有学上 8 人赞同了该文章 在之前的Lecture 1当中介绍了NS方程的第一性原理推导,Lecture 2当中我们研究了NS方程的Local-wellposeness,Lecture 3将研究weak solutions,陶神的原notes见 Weak solutions of the Navier-Stokes equationsterrytao....
Navier-Stokes equationsThe main assumption of the so-called 蔚-regularity theory of suitable weak solutions to the Navier-Stokes equations is uniform smallness of certain scale-invariant quantities, which rules out singularities. One of the best results of 蔚-regularity is the famous Caffarelli-Kohn...
Let u be a weak solution of the Navier-Stokes equations in a smooth bounded domain Ω 3 and time interval [0,T), 00. As it is well known, global regularity of u for general u 0 and f is an unsolved problem unless we pose additional assum... R Farwig,H Kozono,H Sohr - 《Engl...
arXiv:2306.07094v1 [math.AP] 12 Jun 2023Weak solutions for steady, fully inhomogeneousgeneralized Navier-Stokes equationsJulius Jeßberger and Michael RůžičkaJune 13, 2023Institute of Applied Mathematics, Albert-Ludwigs-University Freiburg,Ernst-Zermelo-Str. 1, D-79104 Freiburg, GermanyE-...
Today the following problems are open: • (PS) Is there a unique strong (smooth) solution to the Navier-Stokes equations? • (PW) Is a weak solution of the Navier-Stokes equations unique? The Clay Prize Problem concerns the mathematical proof of existence (or non- existence) of strong...
内容提示: CONDITIONS IMPLYING ENERGY EQUALITY FOR WEAK SOLUTIONS OF THENAVIER–STOKES EQUATIONSTREVOR M. LESLIE AND ROMAN SHVYDKOYA BSTRACT . When a Leray–Hopf weak solution to the NSE has a singularity set S of dimension d lessthan 3—for example, a suitable weak solution—we f ind a ...
Uniqueness Of Weak Solutions Of The Navier-stokes Equationsnavier-stokes equationssolution uniquenessweak leray-hopf solutionmultiplier spaceConsider the Navier-Stokes equation with the initial data a ∈ L_σ~2(R~d). Let u and v be two weak solutions with the same initial value a. If u ...
In this note we consider the inviscid limit for the 3D Boussinesq equations without diffusion, under slip boundary conditions of Navier's type. We first study more closely the Navier-Stokes equations, to better understand the problem. The role of the initial data is also emphasized in connection...
Using common abuse of definitions we equivalently allow to say that a function u ∈ L 2 loc (Q) 3 is a weak solution of the Navier-Stokes system in Q if there is p ∈ D (Q), such that (u, p) is a weak solution in the sense of the above definition. In other words ...
Consider the stationary Navier-Stokes equations in an exterior domain Ω ⊂ ℝ3with smooth boundary. For every prescribed constant vector u∞≠ 0 and every external force f ∈ Ḣ2-1(Ω), Leray (J. Math. Pures. Appl., 9:1-82, 1933) constructed a weak solution u with ...