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A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover,...
We are interested in a barotropic motion of the non-Newtonian bipolar
fluids .
We consider a special
case where the stress tensor is expressed in the form of
potentials depending on eii and .
We prove the
asymptotic stability of the rest state under the assumption
of the regularity of the potential forces.
The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on and . For this case, we prove the existence and uniqueness of weak solution.
We study compressible isentropic Navier-Stokes-Poisson equations in . With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.
We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential inequalities.
We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.
We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [J.L. Bona, T. Colin and D. Lannes, Arch. Ration. Mech. Anal. 178 (2005) 373–410] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussinesq system displayed in [W. Choi...
We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [J.L. Bona, T. Colin and D. Lannes,
Arch. Ration. Mech. Anal.178 (2005) 373–410] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussinesq system displayed in [W. Choi...
Ω being a bounded open set in R∙, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Yt, t ≥ 0). More precisely: Eω0(〈h,Yt〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
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