We prove that a solution to Navier-Stokes equations is in L-2(0, infinity: H-2(Ohm)) under the critical assumption that u is an element of L-r,L-r', 3/r + 2/r' less than or equal to 1 with r greater than or equal to 3. A boundary L-infinity estimate For the solution ...
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.wordpress.com/2018/10/02/254a-notes-2-weak-solutions-of-the-navier-stokes-equations/ 之前知...
A pair (u,p) is a suitable weak solution to the Navier–Stokes equation (1.1) if u is a Leray–Hopf weak solution, p∈L43(0,T;L#2), and the local energy inequality(2.3)∫0T∫T3|∇u|2ϕdxdt≤∫0T∫T3[|u|22(∂tϕ+Δϕ)+(|u|22+p)u⋅∇ϕ]dxdt holds for al...
Consider the stationary Navier-Stokes equations in an exterior domain Ω ⊂ ℝ3 with 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 ...
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 ...
arXiv:2502.17147v1 [math.AP] 24 Feb 2025GLOBAL WEAK SOLUTIONS OF THE NAVIER-STOKES-KORTEWEGEQUATIONS IN ONE DIMENSIONPAOLO ANTONELLI, DIDIER BRESCH, AND STEFANO SPIRITOAbstract. We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg(NSK) equations when the ...
Navier-Stokes equationhalf-spacelocal weak solutionvacuumIn this paper, we establish the local existence of weak solutions with higher regularity of the three-dimensional half-space compressible isentropic Navier-Stokes equations with the adiabatic exponent γ > 1 in the presence of vacuum. Here we ...
Non-even positive solutions of the one-dimensional p-Laplace Emden-Fowler equation ON THE REGULARITY AND UNIQUENESS OF WEAK SOLUTIONS FOR THE NAVIER-STOKES EQUATIONS self organized criticality in an one dimensional magnetized grid. application to grb x-ray afterglows Asymptotics for Large Time of Glob...
We want to prove next that the maximum norm of the density controls the breakdown of weak solutions of the Navier-Stokes equations when N = 2. In other words, if a solution of the Navier-Stokes equations is initially suitably smooth and loses its regularity at some later time, then the ...
The uniqueness of weak solutions is, as is well known, an open problem for the generalized Navier–Stokes problem (without damping) for values of q ≤ 2. By adapting [17, Th´eor´eme 2.5.2], we can prove the weak solution to the problem (1.1)–(1.4) is unique under more ...