Abstract
In terms of the sharp Gagliardo–Nirenberg–Sobolev inequalities, we find the precisely sharp criteria of blow-up and global existence for the cubic nonlinear beam equations with L^{2} critical nonlinearities. And we further study the limiting profile of blow-up solutions.
Highlights
1 Introduction The nonlinear beam equation is a class of fourth-order partial differential equations appearing in different physical settings, and it models the weak interactions of dispersive waves in [1] and the motion of the clamped plate and beams in [20]
In terms of the sharp criteria for the nonlinear Schrödinger equation in [8, 14, 16, 19, 23, 36], we study the sharp criteria for the nonlinear Beam equation
We extend the sharp criteria argument in [14, 16] for nonlinear Schrödinger equations to that for the nonlinear beam equation (1.1)
Summary
The nonlinear beam equation is a class of fourth-order partial differential equations appearing in different physical settings (see [26, 27] for a review), and it models the weak interactions of dispersive waves in [1] and the motion of the clamped plate and beams in [20]. The nonlinear beam equation is in the following form:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
