Results 281 to 290 of about 11,370,086 (322)

Paralinearization of the Muskat Equation and Application to the Cauchy Problem

Archive for Rational Mechanics and Analysis, 2019
We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-posedness of the Cauchy problem for rough initial data, in homogeneous Sobolev
T. Alazard, O. Lazar
semanticscholar   +1 more source

On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

, 2017
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates.
R. Mikulevičius, C. Phonsom
semanticscholar   +1 more source

On the Cauchy problem for Boltzmann equations: global existence and weak stability

, 1989
We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution.
R. J. Diperna, P. Lions
semanticscholar   +1 more source

On the Cauchy Problem for Axi-Symmetric Vortex Rings

, 2013
We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry.
Hao Feng, V. Sverák
semanticscholar   +1 more source

Cauchy Problem

An Introduction to Mathematical Relativity, 2021
José Natário
semanticscholar   +1 more source

Cauchy Problem for Dissipative Hölder Solutions to the Incompressible Euler Equations

, 2013
We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or Hölder continuous for any exponent $${\theta < \frac{1}{16 ...
S. Daneri
semanticscholar   +1 more source

On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations

, 1977
Solutions to the Cauchy problem for the equation iu t =Δu+F(|u|  2 )u (x∈ n , t>0), u(x,0)=φ(x), are considered. Conditions on φ and F are given so that, for solutions with nonpositive energy, the following obtains: There exists a finite time T ...
R. Glassey
semanticscholar   +1 more source

The Cauchy Problem

Introduction to Infinite-Dimensional Systems Theory, 2020
Ruth Curtain, Hans Zwart
semanticscholar   +1 more source

Inverse Cauchy problem of annulus domains in the framework of spectral meshless radial point interpolation

Engineering computations, 2017
E. Shivanian, A. Jafarabadi
semanticscholar   +1 more source

The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation

, 2019
Fan Yang, Pan Zhang, Xiao-xiao Li
semanticscholar   +1 more source