ﻻ يوجد ملخص باللغة العربية
In this paper, we prove the global existence for some 4-D quasilinear wave equations with small, radial data in $H^{3}times H^{2}$. The main idea is to exploit local energy estimates with variable coefficients, together with the trace estimates.
Hormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in $(1+4)-$dimensions of the form $Box u = Q(u, u, u)$ where $Q$ vanishes to second order and $(partial_u^2 Q)(0,0,0)=0$. Without the latter
We study the global existence of solutions to semilinear damped wave equations in the scattering case with derivative power-type nonlinearity on (1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea is to exploit local energ
We study the asymptotic behavior of solutions to wave equations with a structural damping term [ u_{tt}-Delta u+Delta^2 u_t=0, qquad u(0,x)=u_0(x), ,,, u_t(0,x)=u_1(x), ] in the whole space. New thresholds are reported in this paper that indicate whi
We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove almost global e
In three previous papers by the two first authors, classes of initial data to the three dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitr