• Corpus ID: 245837697

Schr\"odinger-improved Boussinesq system in two space dimensions

@inproceedings{Ozawa2022SchrodingerimprovedBS,
  title={Schr\"odinger-improved Boussinesq system in two space dimensions},
  author={Tohru Ozawa and Kenta Tomioka},
  year={2022}
}
We study the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimentional domain. Under natural assumptions on the data without smallness, we prove the existence and uniqueness of global strong solutions. Moreover, we consider the vanishing ”improvement” limit of global solusions as the coefficient of the linear term of the highest order in the equation of ion sound waves tends to zero. Under the same smallness assumption on the data as in the Zakharov case, solutions in… 

References

SHOWING 1-10 OF 57 REFERENCES

On the 2D Zakharov system with L2 Schrödinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L2 × H−1/2 × H−3/2. This is the space of optimal regularity in the sense that the

On the Cauchy Problem for Schro"dinger-improved Boussinesq equations

The Cauchy problem for a coupled system of Schr\"odinger and improved Boussinesq equations is studied. Local well-posedness is proved in $L^2(\R^n)$ for $n\le 3$. Global well-posedness is proved in

Zakharov system in two space dimensions

Energy convergence for singular limits of Zakharov type systems

We prove existence and uniqueness of solutions to the Klein–Gordon–Zakharov system in the energy space H1×L2 on some time interval which is uniform with respect to two large parameters c and α. These

Uniqueness of solutions for zakharov systems

We prove that the weak solution of the Cauchy problem for the Klein-Gordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in some larger space

Low regularity global well-posedness for the two-dimensional Zakharov system

Abstract The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L2-norm of the Schrödinger part is small enough. The proof uses a refined

Global existence on nonlinear Schr\"{o}dinger-IMBq equations

In this paper, we consider the Cauchy problem of Schr\"{o}dinger-IMBq equations in $\mathbb{R}^n, n \ge 1$. We first show the global existence and blowup criterion of solutions in the energy space

On the Zakharov and Zakharov-Schulman Systems

Abstract We consider the initial value problem for the Zakharov system [formula] which models the long wave Langmuir turbulence in a plasma. Using the standard iteration scheme in the original system
...