Stability of Blow-Up Profile and Lower Bounds for Blow-Up Rate for the Critical Generalized KdV Equation
نویسندگان
چکیده
منابع مشابه
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
The generalized Korteweg-de Vries equations are a class of Hamiltonian systems in infinite dimension derived from the KdV equation where the quadratic term is replaced by a higher order power term. These equations have two conservation laws in the energy space H1 (L2 norm and energy). We consider in this paper the critical generalized KdV equation, which corresponds to the smallest power of the...
متن کاملBlow up in Finite Time and Dynamics of Blow up Solutions for the L–critical Generalized Kdv Equation
In this paper, we are interested in the phenomenon of blow up in finite time (or formation of singularity in finite time) of solutions of the critical generalized KdV equation. Few results are known in the context of partial differential equations with a Hamiltonian structure. For the semilinear wave equation, or more generally for hyperbolic systems, the finite speed of propagation allows one ...
متن کاملBlow up Dynamic and Upper Bound on the Blow up Rate for critical nonlinear Schrödinger Equation
We consider the critical nonlinear Schrödinger equation iut = −∆u − |u| 4 N u with initial condition u(0, x) = u0 in dimension N . For u0 ∈ H1, local existence in time of solutions on an interval [0, T ) is known, and there exists finite time blow up solutions, that is u0 such that limt→T<+∞ |ux(t)|L2 = +∞. This is the smallest power in the nonlinearity for which blow up occurs, and is critical...
متن کاملExistence of Blow-up Solutions in the Energy Space for the Critical Generalized Kdv Equation
From these conservation laws, H appears as an energy space, so that it is a natural space in which to study the solutions. Note that p = 2 is a special case for equation (2). Indeed, from the integrability theory (see Lax [14]), we have for suitable u0 (u0 and its derivatives with fast decay at infinity) an infinite number of conservation laws. The general question is to understand the dynamics...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2002
ISSN: 0003-486X
DOI: 10.2307/3062156