Strong Trajectory and Global W-attractors for the Damped-driven Euler System in R
نویسندگان
چکیده
We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space H. A similar result on the strong attraction holds in the spaces H ∩ {u : ‖ curlu‖Lp < ∞} for p ≥ 2.
منابع مشابه
Inviscid limit for damped and driven incompressible Navier-Stokes equations in R
We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in R. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstro...
متن کاملN ov 2 00 6 Inviscid limit for damped and driven incompressible Navier - Stokes equations in R 2
We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in R 2. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enst...
متن کاملNumerical solution of second-order stochastic differential equations with Gaussian random parameters
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...
متن کاملRegularity of the global attractor for semilinear damped wave equations
utt + 2ηA 1 2 ut + aut + Au = f(u) in H1 0 (Ω)×L2(Ω), where Ω is a bounded smooth domain in R3. For dissipative nonlinearity f ∈ C2(R,R) satisfying |f ′′(s)| ≤ c(1 + |s|) with some c > 0, we prove that the family of attractors {Aη , η ≥ 0} is upper semicontinuous at η = 0 in H1+s(Ω)×Hs(Ω) for any s ∈ (0, 1). For dissipative f ∈ C3(R,R) satisfying lim|s|→∞ f ′′(s) s = 0 we prove that the attract...
متن کاملGPS Jamming Detection in UAV Navigation Using Visual Odometry and HOD Trajectory Descriptor
Auto-navigating of unmanned aerial vehicles (UAV) in the outdoor environment is performed by using the Global positioning system (GPS) receiver. The power of the GPS signal on the earth surface is very low. This can affect the performance of GPS receivers in the environments contaminated with the other source of radio frequency interference (RFI). GPS jamming and spoofing are the most serious a...
متن کامل