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 equations之前…
We show the existence of global weak solutions to the three dimensional Navier–Stokes equations with initial velocity in the weighted spaces \\(L^2_{w_\\gamma }\\), where \\(w_\\gamma (x)=(1+\\vert x\\vert )^{-\\gamma }\\) and \\(0<\\gamma \\leqq 2\\), using new ...
• (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 solutions, which we may summarize in ...
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 ...
The governing equations consist of the stationary Navier–Stokes equations describing the compressible fluid flows and the stationary Cahn–Hilliard-type diffuse equation for the mass concentration difference. We prove the existence of weak solutions when the adiabatic exponent γ satisfies γ>43. The ...
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...
We consider the Navier-Stokes-Poisson equation in a bounded domain. This system describes the motion of compressible viscous isentropic gas flow under the self-gravitational force. We give an existence theorem of a finite energy weak solution. Our results can be regarded as a generalization of E...
KeyWords:CompressibleNavier—Stokesequations;weaksolutions;globalexistence 1 Introduction Considertheone—dimensional(1D)compressibleNavier—Stokesequationswithdensity— dependentviscositycoeficients: pt+(pu)=0, (pu)f+(』 0“+P(』 D))=((JO)M) (1.1) ...
We consider the stationary Oseen and Navier–Stokes equations in a bounded connected domain of class C1,1 of R3. Here we give a new and simpler proof of the existence of very weak solutions (u,q)∈Lp(Ω)×W−1,p(Ω) corresponding to boundary data in W−1/p,p(Γ). These soluti...
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 ...