On the support of solutions to the Ostrovsky equation with negative dispersion

In this article we prove that sufficiently smooth solutions of the Ostrovsky equation with negative dispersion:

     

On the support of solutions to the Zakharov-Kuznetsov equation

In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation:

     

Cauchy problem for the Ostrovsky equation in spaces of low regularity

In this article we consider the initial value problem for the Ostrovsky equation:

     

On the support of solutions to the Ostrovsky equation with positive dispersion

In this paper we prove that sufficiently smooth solutions of the Ostrovsky equation with positive dispersion,

     

On the regularity of the Navier-Stokes equation in a thin periodic domain

We address the global regularity of solutions of the Navier-Stokes equations in a thin domain Ω=[0,L₁]×[0,L₂]×[0,?] with periodic boundary conditions, where L₁,L₂>0 and ?∈(0,1/2). We prove that if

     

Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation

     

The local variational principle of topological pressure for sub-additive potentials

Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:

     

Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition

Let p>1 and Ω be a smoothly bounded domain in . This paper is concerned with a Cauchy-Neumann problem

     

Uniqueness properties of solutions of Schrödinger equations

Under suitable assumptions on the potentials V and a, we prove that if u∈C([0,1],H¹) is a solution of the linear Schrödinger equation

     

A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure

In this paper we investigate the pseudoparabolic equation

     

New results of general n-dimensional incompressible Navier-Stokes equations

Let u=u(x,t,u₀) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations

     

Parabolic approach to nonlinear elliptic eigenvalue problems

We consider the asymptotic profiles of the nonlinear parabolic flows ut=Δum to show the geometric properties of the following elliptic nonlinear eigenvalue problems:

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN: