1,721,037 research outputs found
THE OBERBECK–BOUSSINESQ SYSTEM WITH NON-LOCAL BOUNDARY CONDITIONS
No full textWe consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of the full Navier–Stokes–Fourier system in the regime of low Mach and low Froude numbers. The existence of strong solutions is shown on a maximal time interval [0, Tmax). Moreover, Tmax = ∞ in the two-dimensional settin
On a class of generalized solutions to equations describing incompressible viscous fluids
No full textOn the Motion of a Compressible Viscous Fluid Driven by Time Periodic Inflow/Outflow Boundary Conditions
No full textWe consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic solution in the class of weak solutions satisfying the energy inequality
On the Motion of a Compressible Viscous Fluid Driven by Time Periodic Inflow/Outflow Boundary Conditions
No full textWe consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic solution in the class of weak solutions satisfying the energy inequality
On Strong Continuity of Weak Solutions to the Compressible Euler System
No full textLet S = {tau(n)}(n=1)(infinity) subset of (0, T) be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions that are not strongly continuous at each tau(n) , n=1,2, .... The proof is based on a refined version of the oscillatory lemma of De Lellis and Szekelyhidi with coefficients that may be discontinuous on a set of zero Lebesgue measure
Ill-posedness for the full euler system driven by multiplicative white noise
Get PDFWe consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem is ill posed-there exist infinitely many global in time weak solutions. The solutions are adapted to the noise and satisfy the entropy admissibility criterion
On the Vanishing Electron-Mass Limit in Plasma Hydrodynamics in Unbounded Media
No full textWe consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system
On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions
No full textWe study the low Mach number limit for the compressible Navier-Stokes system supplemented with Navier's boundary condition on an unbounded domain with compact boundary. Our main result asserts that the velocities converge pointwise to a solenoidal vector field - a weak solution of the incompressible Navier-Stokes system - while the fluid density becomes constant. The proof is based on a variant of local energy decay property for the underlying acoustic equation established by Kato
Scale analysis of a hydrodynamic model of plasma
No full textWe examine a hydrodynamic model of the motion of ions in plasma in the regime of small Debye length, a small ratio of the ion/electron temperature, and high Reynolds number. We analyze the associated singular limit and identify the limit problem — the incompressible Euler system. The result leans on careful analysis of the oscillatory component of the solutions by means of Fourier analysis
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