## 58 Citations

On Uniquenes Properties of Solutions to the Benjamin-Ono Equation

- Mathematics
- 2011

This talk is concerned with some special uniqueness properties of solutions to the IVP associated to the Benjamin-Ono equation. These will be deduced as a consequence of some persistent properties in…

The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces

- Mathematics
- 2019

The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces

- Mathematics
- 2016

The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces

- Mathematics
- 2013

On the Cauchy problem associated to a regularized Benjamin-Ono--Zakharov-Kuznetsov (rBO-ZK) type equation

- Mathematics
- 2018

In this work we shall study the well-posedness and ill-posedness of the Cauchy problem associated to the equation \begin{equation*} u_{t}+a(u^{n})_{x}+(b\mathscr{H} u_{t}+u_{yy})_{x}=0,…

On Decay Properties of Solutions to the IVP for the Benjamin–Ono Equation

- Mathematics
- 2013

In this work we investigate unique continuation properties of solutions to the initial value problem associated to the Benjamin–Ono equation in weighted Sobolev spaces $$Z_{s,r}=H^s(\mathbb R )\cap…

Unconditional uniqueness for the Benjamin-Ono equation

- Mathematics
- 2021

We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in H, both on the real line and on the torus. We use the gauge transformation of Tao and two…

Well-posedness for the two dimensional generalized Zakharov-Kuznetsov equation in weighted Sobolev spaces

- Mathematics
- 2014

We consider the well-posedness of the initial value problem associated to the k-generalized Zakharov-Kuznetsov equation in fractional weighted Sobolev spaces. Our method of proof is based on the…

Continuity and Analyticity for the Generalized Benjamin-Ono Equation

- MathematicsSymmetry
- 2021

By the symmetry of the spatial variable, a lower bound of the lifespan and the continuity of the data-to-solution map is obtained and the Gevrey regularity and analyticity for the g-BO equation is proved.

## References

SHOWING 1-10 OF 66 REFERENCES

The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

- Mathematics
- 2010

In a recent work, Ionescu and Kenig proved that the Cauchy problem associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$. In this paper we give a simpler proof of Ionescu and…

GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R)

- Mathematics
- 2004

We show that the Benjamin–Ono equation is globally well-posed in Hs(R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly…

Well-posedness results for the generalized Benjamin-Ono equation with arbitrary large initial data

- Mathematics
- 2004

We prove new local well-posedness results for the generalized Benjamin-Ono equation (GBO) ∂tu+ℋ∂x2u+uk∂xu=0, k ≥ 2. By combining a gauge transformation with dispersive estimates, we establish the…

Benjamin–Ono Equation with Unbounded Data☆

- Mathematics
- 2000

Abstract The initial value problem (IVP) for the Benjamin–Ono equation with unbounded initial data is considered. We show existence and uniqueness of global solutions for sublinear growth data. The…

On well-posedness for the Benjamin–Ono equation

- Mathematics
- 2005

We prove existence and uniqueness of solutions for the Benjamin–Ono equation with data in $$H^{s}({\mathbb{R}})$$ , s > 1/4. Moreover, the flow is hölder continuous in weaker topologies.

Well-posedness for the Generalized Benjamin–Ono Equations with Arbitrary Large Initial Data in the Critical Space

- Mathematics
- 2008

We prove the local well-posedness of the generalized Benjamin-Ono equations , k ≥ 4, in the scaling invariant spaces where s k = 1/2 − 1/ k. Our results also hold in the nonhomogeneous spaces . In…

Global well-posedness of the Benjamin-Ono equation in H^1(R)

- Mathematics
- 2003

We show that the Benjamin-Ono equation is globally well-posed in $H^s(\R)$ for $s \geq 1$. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be…

On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations

- Mathematics
- 2003

We prove that the Benjamin-Ono equation is locally well-posed in Hs(R) for s > 9/8 and that for arbitrary initial data, the modified (cubic nonlinearity) Benjamin-Ono equation is locally well-posed…

Ill-Posedness Issues for the Benjamin-Ono and Related Equations

- MathematicsSIAM J. Math. Anal.
- 2001

We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de…