Yuusuke Sugiyama

activity

20172022

collaborators

5 papers

math.AP2022

Local solvability for a quasilinear wave equation with the far field degeneracy: 1D case

Yuusuke Sugiyama

We study the Cauchy problem for the quasilinear wave equation $\partial_{t}^{2} u = u^{2 a} \partial_{x}^{2} u + F (u) u_{x}$ with $a \geq 0$ and show a result for the local in time existen…

math.AP2022

Formation of singularities for a family of 1D quasilinear wave equations

Yuusuke Sugiyama

We consider the blow-up of solutions to the following parameterized nonlinear wave equation: $u_{tt} = c (u)^{2} u_{xx} + λ c (u) c^{'} (u) (u_{x})^{2}$ with the real parameter $λ$ . In previo…

math.AP2019

Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping

Yuusuke Sugiyama

In this paper, we consider the 1D compressible Euler equation with the damping coefficient $λ / (1 + t)^{μ}$ . Under the assumption that $0 \leq μ < 1$ and $λ > 0$ or $μ = 1$ and $λ > 2$ , we prov…

math.AP2018

Spatial-decay of solutions to the quasi-geostrophic equation with the critical and the super-critical dissipation

Masakazu Yamamoto, Yuusuke Sugiyama

The initial value problem for the two dimensional dissipative quasi-geostrophic equation derived from geophisical fluid dynamics is studied. The dissipation of this equation is giv…

math.AP2017

Existence and nonexistence theorems for global weak solutions to quasilinear wave equations for the elasticity

Yun-guang Lu, Yuusuke Sugiyama

In this paper, by using the theory of compensated compactness coupled with the kinetic formulation by Lions, Perthame, Souganidis and Tadmor \cite{LPT,LPS}, we prove the existence…