AbstractThis paper is concerned with the existence and uniqueness questions on weak solutions of the stationary Navier–Stokes equations in an exterior domain Ω in R3, where the external force is given by divF with F=F(x)=(Fji(x))i,j=1,2,3. First, we prove the existence and uniqueness of a weak solution for F∈L3/2,∞(Ω)∩Lp,q(Ω) with 3/2<p<3 and 1≤q≤∞ provided ‖F‖L3/2,∞(Ω) is sufficiently small. Here Lp,q(Ω) denotes the well-known Lorentz space. We next show that weak solutions satisfying the energy inequality are unique for F∈L3/2,∞(Ω)∩L2(Ω) under the same smallness condition on ‖F‖L3/2,∞(Ω). This result provides a complete answer to the uniqueness question of weak solutions satisfying the energy inequality, the existence of which was proved ...
AbstractThe Navier problem is to find a solution of the steady-state Navier–Stokes equations such th...
One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equatio...
AbstractIn a recent work [P.G. Lemarié-Rieusset, Uniqueness for the Navier–Stokes problem: Remarks o...
AbstractExtending the notion of very weak solutions, developed recently in the three-dimensional cas...
The paper concerns the existence of weak solutions to the 3d-Navier–Stokes initial boundary value pr...
The paper concerns the existence of weak solutions to the 3d-Navier–Stokes initial boundary value pr...
AbstractWe consider the three-dimensional exterior problem for stationary Navier–Stokes equations. W...
AbstractWe exhibit simple sufficient conditions which give weak–strong uniqueness for the 3D Navier–...
AbstractWe consider the Navier–Stokes equations on thin 3D domains Qε=Ω×(0, ε), supplemented mainly ...
AbstractThis paper is concerned with the existence and uniqueness questions on weak solutions of the...
We consider the stationary Oseen and Navier–Stokes equations in a bounded connected domain of class...
We prove that in a bounded Lipschitz domain of $R^3$ the steady-state Navier–Stokes equations with b...
AbstractThe weak solution to the Navier–Stokes equations in a bounded domain D⊂R3 with a smooth boun...
AbstractIn this paper, we show that the Cauchy problem of the Navier–Stokes equations with damping α...
The Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the n...
AbstractThe Navier problem is to find a solution of the steady-state Navier–Stokes equations such th...
One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equatio...
AbstractIn a recent work [P.G. Lemarié-Rieusset, Uniqueness for the Navier–Stokes problem: Remarks o...
AbstractExtending the notion of very weak solutions, developed recently in the three-dimensional cas...
The paper concerns the existence of weak solutions to the 3d-Navier–Stokes initial boundary value pr...
The paper concerns the existence of weak solutions to the 3d-Navier–Stokes initial boundary value pr...
AbstractWe consider the three-dimensional exterior problem for stationary Navier–Stokes equations. W...
AbstractWe exhibit simple sufficient conditions which give weak–strong uniqueness for the 3D Navier–...
AbstractWe consider the Navier–Stokes equations on thin 3D domains Qε=Ω×(0, ε), supplemented mainly ...
AbstractThis paper is concerned with the existence and uniqueness questions on weak solutions of the...
We consider the stationary Oseen and Navier–Stokes equations in a bounded connected domain of class...
We prove that in a bounded Lipschitz domain of $R^3$ the steady-state Navier–Stokes equations with b...
AbstractThe weak solution to the Navier–Stokes equations in a bounded domain D⊂R3 with a smooth boun...
AbstractIn this paper, we show that the Cauchy problem of the Navier–Stokes equations with damping α...
The Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the n...
AbstractThe Navier problem is to find a solution of the steady-state Navier–Stokes equations such th...
One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equatio...
AbstractIn a recent work [P.G. Lemarié-Rieusset, Uniqueness for the Navier–Stokes problem: Remarks o...