1,721,000 research outputs found
Vanishing dielectric constant regime for the Navier Stokes Maxwell equations
No full textIn this paper we rigorously justify the convergence of smooth solutions of the Navier-Stokes-Maxwell equations towards smooth solutions of the classical 2D parabolic MHD equations in the case of vanishing dielectric constant. The result is achieved by means of higher-order energy estimates
Renormalized solutions of the 2D Euler equations
Full text linkIn this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized
Solutions of the Navier-Stokes equations constructed by artifi cial compressibility approximation are suitable
No full textIn this paper we prove that weak solution constructed by artificial compressibility method are suitable in the sense of Scheffer, [18], [19]. Using Hilbertian setting and Fourier transform with respect to the time we obtain non- trivial estimates for the pressure and the time derivative of the velocity field which allow us to pass into the limi
Strong convergence of the vorticity and conservation of the energy for the α-Euler equations
Full text linkIn this paper, we study the convergence of solutions of the alpha-Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity omega(0 )in L-x(p) for p is an element of (1,infinity), we prove strong convergence in L-t infinity L-x(p) of the vorticities q alpha , solutions of the alpha-Euler equations, towards a Lagrangian and energy-conserving solution of the Euler equations. Furthermore, if we consider solutions with bounded initial vorticity, we prove a quantitative rate of convergence of q(alpha) to omega in L-p , for p is an element of (1,infinity)
Renormalized solutions to the continuity equation with an integrable damping term
Full text linkWe consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511–547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed in the class of distributional solutions and the solution is transported by suitable characteristics of the vector field. In this paper, we prove existence and uniqueness of renormalized solutions in the case of an integrable damping term, employing a new logarithmic estimate inspired by analogous ideas of Ambrosio et al. (Rendiconti del Seminario Fisico Matematico di Padova 114:29–50, 2005), Crippa and De Lellis (J Reine Angew Math 616:15–46, 2008) in the Lagrangian case
Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations
Full text linkThe aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with L-p initial vorticity, provided that p >= 4. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order | log nu|^(-alpha/2) with alpha > 0
Strong continuity for the 2D Euler equations
Full text linkWe prove two results of strong continuity with respect to the initial datum for bounded solutions to the Euler equations in vorticity form. The first result provides sequential continuity and holds for a general bounded solution. The second result provides uniform continuity and is restricted to Hölder continuous solutions
WEAK SOLUTIONS OF NAVIER–STOKES EQUATIONS CONSTRUCTED BY ARTIFICIAL COMPRESSIBILITY METHOD ARE SUITABLE
No full text We prove that weak solutions constructed by artificial compressibility method are suitable in the sense of Scheffer. Using Hilbertian setting and Fourier transform with respect to time, we obtain non-trivial estimates on the pressure and the time derivative which allow us to pass to the limit. </jats:p
On the Vanishing viscosity limit of 3D Navier-Stokes equations under slip boundary conditions in general domains
No full textWe consider the vanishing-viscosity limit for the Navier-Stokes equations with certain slip-without-friction boundary conditions in a bounded domain with non-flat boundary. In particular, we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary. The proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity
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