7 research outputs found
Decay rates for the 4D energy-critical nonlinear heat equation
In this paper we address the decay of solutions to the four-dimen\-sional
energy-critical nonlinear heat equation in the critical space .
Recently, it was proven that the norm of solutions goes to zero
when time goes to infinity, but no decay rates were established. By means of
the Fourier Splitting Method and using properties arising from the scale
invariance, we obtain an algebraic upper bound for the decay rate of solutions.Comment: 13 pages. arXiv admin note: text overlap with arXiv:2206.0944
Algebraic decay rates for 3D Navier-Stokes and Navier-Stokes-Coriolis equations in
An algebraic upper bound for the decay rate of solutions to the Navier-Stokes
and Navier-Stokes-Coriolis equations in the critical space is derived using the Fourier Splitting Method.
Estimates are framed in terms of the decay character of initial data, leading
to solutions with algebraic decay and showing in detail the roles played by the
linear and nonlinear parts.Comment: 20 pages. Title changed. Emphasis placed on new estimates in critical
spac
Global well-posedness for a family of regularized Benjamin-type equations
In this work we prove local and global well-posedness results for the Cauchy
problem of a family of regularized nonlinear Benjamin-type equations in both
periodic and nonperiodic Sobolev spaces.Comment: 22 page
Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
We address the decay of the norm of weak solutions to the 2D dissipative
quasi-geostrophic equation. When the initial data is in only, we prove
that the norm tends to zero but with no uniform rate, that is, there are
solutions with arbitrarily slow decay. For the initial data in ,
with , we are able to obtain a uniform decay rate in . We
also prove that when the norm of the initial data
is small enough, the norms, for have uniform
decay rates. This result allows us to prove decay for the norms, for , when the initial data is in .Comment: A paragraph describing work by Carrillo and Ferreira proving results
directly related to the ones in this paper is added in the Introduction. Rest
of the article remains unchange
Large Time Behavior of the Navier-Stokes Flow
International audienceDifferent results related to the asymptotic behavior of incompressible fluid equations are analyzed as time tends to infinity. The main focus is on the solutions to the Navier-Stokes equations, but in the final section a brief discussion is added on solutions to Magneto-Hydrodynamics, Liquid crystals, Quasi-Geostrophic and Boussinesq equations. Consideration is given to results on decay, asymptotic profiles, and stability for finite and nonfinite energy solutions